{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Depth: Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The *k*-means clustering model explored in the previous chapter is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n",
    "In particular, the nonprobabilistic nature of *k*-means and its use of simple distance from cluster center to assign cluster membership leads to poor performance for many real-world situations.\n",
    "In this chapter we will take a look at Gaussian mixture models, which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "deletable": true,
    "editable": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Motivating Gaussian Mixtures: Weaknesses of k-Means\n",
    "\n",
    "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n",
    "As we saw in the previous chapter, given simple, well-separated data, *k*-means finds suitable clustering results.\n",
    "\n",
    "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Generate some data\n",
    "from sklearn.datasets import make_blobs\n",
    "X, y_true = make_blobs(n_samples=400, centers=4,\n",
    "                       cluster_std=0.60, random_state=0)\n",
    "X = X[:, ::-1] # flip axes for better plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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cW0XBqpqJNtt5pe/VbM9LJcdTiN1k5flNP4a1qbKhoFqHYxLkvUjwQh5gHXXCzSkLocQh6n+L9G7xx9tN7RGmdki9ALQDYU4ygS8JLP1OrLEGdYoa4bA7RoefKbaJaBi2TLwq+Xx3YFuukmhS55A7hzf6Xsu+wgxSnFm0j2rMkAadmJ/6Lz8mrybVmYWCCDnLbuqIJd4SxcbsZK5Y9gZdY5pzX5dzmbl3edjiHRXB5LYjqvIWayzCcQXSuxZcfwCyeFFPxL6NUGpu5oswdwZz5xIbLIAKIRpDI91ILbsaV0IMTgVqhMO2KCbuSziXZzf9iFv3IvGHG8yKWmZn8qoiI0wl4RFUFDI8+Uxo3hfwh1DuXfsZazJ34iyjmCbFmUOKMxutKE67MSeZm1e9T0J0s7BZLC0jGjC6SY9K3EntQwjVH2bwbkO6F4N3E+iHkM5vQdgQlt4n28QgpG8neFaDEgfWEQhhRQgz0n42OOcAx34nvJBzD7prJCL2ZUQpOfUGBuGoEQ4bYFyz3jRz1OPT3YvZX5hBl5jmXN1mGK0jG1Z6zP2FGXyw4w/WZO4m1uzg8tZDGN809I+/R2wr/kj9N2wc2ic12pawZU3mLtZk7irTWfvj1jJoJu3WPPybvS/kOWahMqnN0FLHrZMoMVA4A/Q8wA3etUjXfGTUPSgR15xs6wCQUkPmTAXXAv8GoQIC4j5AWPogoh5G+naDdyshc7XdfyILv0RETDrBlhvUBWqMwwboEdeSF+Oq5ou8Nz+NySum4/R50JEcduXw/Oaf2JSznwmiQ9DxN7Q/g6VpW4IWFsH/BtArrk3Aw2PJoc0hjy2JwN8DMlTYQwf0MEUWPqkzolGX0m+wDiLzXgI9i6MhBYm/IOVFpP1chBK+O8+JQhZ+VuSsixYWi57vMusGaLjcv6gY/zUy/w0oeJfgmbYTCj8Dw2EbVIJanAtWOm9um0dhkbM+gkvzMnv/GtJ8+UHHt4lsyPsDbqJPXJviOKNS1HD3rCY9eaHPlQHHW1VzULHLscSaIzBVIt3OpphIKxGi0aROrtdZ9xsWuBcQMv4rTOBeFrz9ZFD4KcFZIAAS3H8C/lRR/8MlzPdDlh5+MzAIR6Vm2F6vl2nTpnHgwAE8Hg+33noro0bVrNX8NZm7QsaHVaGwxXWI4JIU6BjdlHcG3Aj424Hlep04TFb+TtvGdX+/wwFnBo1tcdzUYRTjmvbiiz1LoRRZ02xvQaWURzR0YswOdKnz4c5FfLH7L5yaFwHEWiIY36Qnl7cZetxZJFJKdhccRiBoHdEgpH7KiaWUh1tNifnqYZyt1EDPPvq3ZQCh70cBy+BqMMzgVKBSDnv27NnExsbywgsvkJ2dzfnnn1/jHLZdtVDgC+7yoiCwl6J8V3ycUIi1RPBT8mpeSppT3PB2d8FhHt/wLbd1HFOqswYq5awF0CuuDQ6TlQfXzWTxoc3FRTkSv5zq53uXMSt5Ja+ddi194ttU4iqwNnMXj6z/hjyfC4kkxuzgqZ6X0TOuVaXGqxJs54BzFkFhBKmBpYbE9C39wF2UzRK077Ti/yvMHZHWM8C9iKOxbAVEBCJyyomw1KAOUqmQyNixY5kyxf+lk1KiqjVk9lOCC1r0x6qEeB4J6GFrGrQ5z+tkX0F6gH6JT9d4Y9u8oO7kLt3LK1t+CSh3ryraRDZkeMMEzlr4NH8c2hi2gtKt+/jvP19WKkxysDCLOxM/4bA7F6fmwaV5OeTK4Y41MzjkyjneW6g0IupOUJuCcBRtMQE2iHm6xhSciKi7QdgJDHfYwDoSYWofeGzsSxB5DyhNQcSAdTyi3g8IU0sMDCqDkMfRqiQ/P59bb72VSy65hAkTJgTsS0xMxOFwhDmz+vFKjZcPL2S76zA+dMyoCCG4q+FI2hCLzebP7XbpXj7M+Ju1hcmowh+VnhDTnbOju3LYm8d/U2ZXi2M+Frswc1lcX1qa43j28O94yqH6ZkHlgcZjaGctvUWYy+Uqvl+AmZmJ/J63pTjN8AgmFMZFd2Fi3MlLoxN4iLIsxWFah0+PJ8czBq8e/IAti8B71og0r8GiJOPRm5Dv7c/xFGJZlH3Ut3+Ow7QJTTrIcp9Dtvsc/DnYR7GpSTSNeAlVyfVboUeSUng3Tl+34mNMIg27aTO6jKTA15PjyQM49nOu69TV+y0sLKRv374h91X625GSksLtt9/OFVdcEeSsj5CQkFDZ4Y+bA4WZZBxy+heApMCLRjNbPCO6nMahXfuLbfvP6hmscx3Ah16czfFz3kZaN27O0vSt1eKsLYoJr65hFgoSuLH9KK5uOwxFKDy0/mu85Zw1q4pCy1YtSSgjjJGUlBTwWWSvWYGWF3wNHzo5Nu2kfm5+ehb/vwaVHOHIPUvtEDLzMn98WbpA2EB8jIj/CmFqUcnRE4CzAL/bb1L0n5JILRWZ/kSRqJUfRXXTMuopRP25oDZD5j4Ozu/8i6oAmBBxHyAsPakMx37OdZ26er+JiYlh91UqJJKens51113H1KlTmThxYqUNqy6klNyV+AmH3Dl4pIZetPy435nJuYtf4JDXP+NJLshgXdbuIBlXl+blnR3zWZe1p1LXF4hSmw30i29LI1sM7aOb8Grfa5jcbkSxeNOBwsxy94NUhEJCTLMK25cQ3RyzEmyfVTGREF3x8WoyMmcqaKkgCwDN/796OjK7euPIsnCmX2MkCB+y8HN/UZDrB8Dtt0kWgMxBZl2HlKGyUAwMKumw33nnHXJzc5k+fTqTJk1i0qRJuFw150u2Iz+V1DCdyD26j3fT/Sli+wrTQzougDyfK2yetSrCi62qKPxfp7NKlWNdlr6NVFc2STkHuCPxY57Y8C2bs/ezOWc/3WNbYCpHRoRFqDzc/SLMoeL0ZTCx5QDMIvg8k6IWqxjWBaSeDZ5EglMFdfBtR2rV2KHHtx0I9f3x+mVXC2aADNXSTS8q0TcwCKZSIZGHHnqIhx56qKptqTKyPAWl5kjv9WSS7SmkpaM+Xj10rNiqmPDovpBz3b5xbdmal0Kh14X3mDiwKgSr0nfgCTm7CkQi0aRkzsG1zDm41q9IKEERAiGP5iEogEmYiLU4kEh6xLbiuvYjK63WV98WzXsDbuTxf79lT75fcL9NZEMe63FxSD3wWot0EnZOItSiWXc1Ye4K7iXAsZlKFjB3B1+YnqLSC3oI5UIDA2pYpWNV0Tm6WVhHDP71fZ/uo0VEPXrGtWZd5u6ART6baub8Zqfx44E1QYJQdtXCxFaD6BHbkltXvc/ugsAOIx6pVTqUcuRaFmGibWQjducfRgjB0Aadmdrl3CpV7+sY3ZQvhtxBlicfgSDWUnNFliqN0hiUWNAPhdhpBrV1lV5O+nYgnT/5c7UtffxiUPIYhy3MfrEr346iQqFjpwSq/1wDgxDUSYcdbbZzeashfLpnScj98aYI6lmjAHi+95XcvupDNufuL97fK7Y1d3Qah1vX+DXlH9yaD4nErloYXL8jPWJb8uehTaSGSYE73lZiHukj0mxj6ZgnUISo1uYEcZY6NKM+BiEERD+OzL6TwOpEC0Q9jCgRFpLS4487O78DdLCdh3BcgVDKl+mkF3wMeS/jzyHXwPUjqO38f/t2AgJMbRAxzyHURhB5J9KzLGBREmxg6YswdwtxBQODOuqwAW7vdBZu6eWbvX+XCC0ILKqJ6+oNKq7qm71/NdvzAmOZ67L28Oa233ig63mMbdqT31I2oEmdMxp15ef9axi76Jlqt/9AYWZRhxwNXWqYwsTaj+DSPGzK3o8mddLcOXh0jQH1OtDUcfL1NyqD9O1G5r3m70YjHGAq0n8xtUM4Li9/LrN1BJh7g3clAV1tPEuR9gkIIZDSh8y8GrybKXbs+a8jXT9BvW8RworUMvwhFLU54pgHqPTth7yXCAh/yEJ/HDtqKsJ+NkiJUI/qsQtzB4j/Cpn3P3+cXTjAcTki8taK/lMZnELUWYcthOCehAlMaHYan+/+i135h+gU3ZSJLQeyYMsq7kn8lBRnNjvyU4POdelevk1eSYuI+sw7uA6P7mN0kx78lrKeBYc2Vt4mRLkzQFo66nNP4qcsT9+GlJLusS15oOt5tItqHHTsD/tW8erWuWhSFme8HGnUO7HlAMbIylVDniykbw8y46KjfR5lFniKGgN4liELv4S4NxHWclQ/uv8E33oCW5B5wP07eM4D6xB/5aJvC4GzcBf49iELPkO6F4J3A6CC4kBGPYJiH1fiGr8Ruq7VBc5vwirzCXMCIn5G2fdgYFBEnXXYR+gY3YQnel4CwIq07Vz/99vl6r+oSZ1XtszBUxQL35mXWq5ilnAMqd+RR7pPZMLi54vHDIdFmNiVf5g8b2FxHvj67L3csPJdZg6ZQiN7bPGxazN38cqWuUHVmEcc9/fJq2gQb6YLtUf9L3RT3iN4AS8y+x6/Ol6IbJeAsZw/HBN2OLKjEOn8EWEdgnTND30MTsh/DX/vxqLPTHdCzv1ItT7iSPcY6SGkaBWU0rDXwKDi1Fm1vmNJzNzFHYkzyt0sV5N6gGM9HmdtUUx0j21JnDWSwQ06h83RNguVpvY4Lmo5ALfuDSracWs+vtobqFr32e6/gpx1SVyal99zkypt+0nBs4LQzrokXvCW522nlM9NFiKdc4tEm8JlFZVw1sW4kPlvHv3TOoLQlZMWsI0vh40GBuWjzs+wwV9Ic0/ipyft+qpQmNDcLwz0aPeJTFv3FYmZu7AUpQ4Ort+RaV0vQApJrDmCZzb9EDIH3Cc11mftDdh2oDCzzOvn6cEiWDWacE15KzOUfQLSvYzgZgIC3AuRnuUgdUKHNEpZN/DtPDqSOQFpPw9cs0vkVltBbYSImHxc9hsYlOSUcNhrM3dTWEazgZLEmB3keZ1ldkEPhUmo6FIv6vIusKomnu11eXFKXoTJymunTeZgYRb7nRm0ctQPCHEANLfXK3bmJREImjsCGwl3j21JckF62BJ6s1DpYa9l1YulNeUtxoxUGiFzn/MXmkgPqA3BNgbhuPjoYdYxIB4OUaQiKa58LOUa/pfQEOESU+C6gIh+AqzDiioc88B6FsJxaY0RrTKoG5wSDntLbphO1sdgEiodoxrzcPeLmPz327iPCTXYFDPxlghSXNkh3WOUauOFPlfRPa4lm3L2YxIqCTHNUEOk5TV1xIXN4DineR8+2rUoaLtVMXFF69MDtl3TdjgLUv8NOSNXUYgw2RgbXbv0FvxNef8p6uyiE1gxaAZUiHoAMs4ragZQFLLwpUD+RmTBe5iV54AE0A8H50JXCJXgxrpWcFyPlLI420gIAbbRCNvo47iWgUHpnBIx7PrW6FJ7w6hCIcZs54rWQ3h3wE20i2rM9e1GYlVMxQp+NtXM4AYd+W7YPcSHyV3O01y8uGUOZsVEr7jWdIttEdJZl0U9axSv9L2aWLMDh2olwmTFoVqYmnAuO/JSuW3Vh9yxZgbzUzbQzBHP2/1voGtMi6KWZGBVzMSYHZzdrA+fDfk/YlR7hW04mQihosS+jKj/PSJ6GkQ/CRG3g2UEOK5E1P/Zn+4ncwiOL2sgc2nsKIox62kgKqvM5wJTazD3BCyAreh/Nci+FZl+JtIV/GA1MKguTokZdqTJGja40SO2JR8MvCVo++R2IxjRqAu/pawnz+eiU1RTBtfvyJ6CNAq08DO25Px0ducfps1xNA8G6BPfll/PmMam7GS8ukan6CZMSfyE7XkpxRWR67P28HvKep7vfSUzBt2KV/ehCCXoIZHJweOy5WQhTO3B1D7kw1a6/yR8iwiJ3bTFL6Kktj2+TA2lPkr8u+i+w5B9E/h24F+IBLRkv4hU3PsI64DKX8PAoJycEg57debOsPuOjROXpGVEfVyal5+SV2NSVJ7XNbrFNC+1lYyqKGR58mlD5Rz22szdzN6/hkLNzahG3RnVuBsmRWXOgbVsz00JyAhxal5WZexkVcZOBtbvUCkhqJOJlF6k85ciiVErRNyIYi2n+JSwltHSRwISoUQiI66Fgk8oPSYeBm0/Us9E6ClIbTfBgk4uZP7LCOvXFR/bwKCC1K5feCWJUK2YhBKye3mkKbwA+kc7F/HdvpW4dV9xufm6rD2lJpw5NQ9N7fGVsvO1Lb/wXfJK3JoXCaxM38HMvct4p/+NzDu4LmT6nlPzsCDlXwbWD+4EX5OR0olMOxf0ElkvnsXollEo8W+XPYB9IhR8QGhFPIHT15FIURQKirjDn7rn+rlokbEhcLh8hmq7kJnXgf3y8A8I7zqk5x+E5eQ1fjA4NTglYtjjmvUOGUu2qxYuahn6VVaXOl/sWRrkJMvKDhYIvk9eWWEbd+Sl8u2+lbiKnDX4nfHOvEP8mLw6bO62QISViK3JyLy3Ap31ETx/oDt/KfN8EXkzmBMA6zF7TCAiOVT4f/7raCmQMboo5c4NWKBC6woaaLsBXynnSWTWZKQvuQLjGhhUnFPCYTd31OPOzmdjUUxYFBMqAoui0iWmOe0ig0u9AQo1D26t4rFPHcmvB9dV+LyFqRvxhgjPuHQvcw+uZULzvthVS9B+q2piXNNeALg1Lx/tXMQFi1/knEXP8VLSz2S68ytsywnBOSv8vvzpZZ4uhB0R/zUibjrYLwVzXzAPgIhbEfV/x6P7u8nI7CmgHSyqZPQBHpDBcgSlo4IS5+/LGG75WvqQhR9XcFwDg4pxSoREAC5qOYDTG3ZmdvJqvtq9FC86STkHmLT8DfrXa8+zva8o1t8AcKgWIkw2cryhSpZL5zjaZIZlRKMu/J7Sgb/Tt+PUPAgEVsXEhGZ96RHXCk3q3Lb6Q7blHiwO33y3byULUzfxWIOxVW7PcSNLyYvX9iGlL0hND1kAIqZYfEkIBaxDwTLAX8giohCm5kVnHEZqqUWCTsf5eUgfwtwR4j9DZpxflEp4LN6iaxkYVB+nxAz7CI1sMSw6tIlC3Ytb91GouXHrPlZl7ODNrfMCjlWEwvXtRhYVwJQfs1AZ06RHhW0b2bhryEVDm2JmfNPeKELh2V5X8EKfq7igeX8uajmAN/tdx9Qu5wKwPG0bO/JSA6RdfVInx1vIH3lbK2xPtWMdXMpOD7LgA8DvqPXM25CHeiAPD0Qe6o1ecLRqVS/8xr898wpk+jj09Av86nkAem7pNoimJWbNKqFnzya/PrXaErRdYB1J6DJ0FUwdS7+egcFxcsrMsMEfJ97vzAyqYHTrPn7cv5o7O48P0J6+tNVgfFLjo51/4tU1vPqx/WUCsSlm6lmjmNxuZIVt6xDVhAtb9ueH5FXFi4521UKbyIbFbbuEEPSv157+9doHnb+yaOZ9LB7dxz/O/UHbTzrRT0LaQkJrfehQ+BlE3oJMPw+0klk+Tsh7Ct27zZ+H7V4QOIYvCZl5BTAdTO1Kt0FYEQ0WIbV9kD4+tC3CAY5rkIcH+v+WOn4BqmOxBJShS98+0A745WDV40vxNDA4winlsDPd+WELWdyaD5/UsZTYL4TgqjbDuKzVEDI9+fyZuolXtv6Cdky2iYIgIboZ45r15pxmfXCY/Ath+wrSWXRoE5rUGdqwc5ktve7qfDbDGiQw+8AaCn0eRjXuxqjG3cqVrhdjtmMSKr4QIlWRyrELcycfRY1Hj3oA8p4l5FKunovuWXeMsy6B65swI+sg84gwr0GIbkj7JHB+GMoCsI30Vyj6tiOFNXS+tsyFnDtDlLYLiqsulWhEzPMIUxukno3M+j+/HKswg/QgbeMQMU8jKl3AY2Dg55Ry2B2jm4RtHdbMER8Qwy6JSVFpaIthwaF/g5w1+COkPeJackmrQcXbZuz8k492LkSTOlL6/57QvC9TEyYUlzMD+HSN31M2MOdAIhLJ2U378HC3i8psWHAs45v14dPdS/AdE661qxbOjOpUobFOFMI6Epn3IsF9DwFzD3DOrdzA0oNFSUVKHaLuBe8y8G0loEumiEFEXF/0ZwPC5//YIOSahAS1jT8MIiIAgZQSmfUf8P4DeOFI93PXPKQSh4j+b+Xux8CgiFMqhh1rieDCFv2xHJMiZ1XM3NW5bBnM0jqhU8IJb8s9yEc7F+HW/bN2DR237mXugbUsT99WfJwmdaYkfszzm39iTeYuEjN387/Ns7l99Yf4ytDMPpZmjnju63IeFsWETTEXZ8Sc36IfPWuo+JMwtQTbWPwl3yWxIaLuA7V+JUc2EW1ZhDzUBQ53B6UpOG72x6GVBmC/BFH/J4TawH+4uUeR0z7252ACtT2BjQ1KoG0D9xxwzURm34LMuumosw7ABYVfoOsVX8A2MCjJKTXDBvxx6lwP8wu3keUpoHVEA/7TaSyDGpS9YDShWV+Scg8ENea1qibOatKz+O+fDySGTNFzah5+2LcKq2JiYepGUl3ZbMjaG7BQ6NK9bMk9yKJDmxhdwcXLCc37MqRBJxYf3lwk29qJFhH1SEqquXrYIuY5pKkTFH7iXyQ0d0dETUVYeoKpFTL/ZSqW5aECbqzqnqLzdPAsBt9GRP3fQ/ZoFEJA3IfI9AuAkhkgPtBK09wuYZd0Ful4h5sDeSBtKDLuI/+9GRhUglPOYStC4azoBO4ccGGFzx3btBe/HlzHxpzkotQ6sKpmzm12Gl1imhcfV+DzhJVm/Td7HysTdwQpAZbEqXn47eD6CjtsgHhrZPEiZW1ACBUReQNE3hC8T4lFRj4M+U9SPqdtAqUJ6KkIUfLfVwM9B5l1E9LSC2E/369TUgLp3UKgs64MbsI3QgBkHjLrBmi4DCGCc+oNDMriuEIi69evZ9Kk0P3q6iImReX1ftfyeI9LGNOkJ+c068urfSdzT8I5AccNb5gQssjFhEKWt6BUZ30Ei3rKPUtDokReBfV+A9sV/s4uEfcUNTgouYBnAdt50GClXxM7ZBaHG7yroOBDZPqF6AUfFe+R3iTImVJFBjciOMRTEh+ycCZ65k3oh/qgHx6Knv820mglZlAOKu0V3n//fWbPno3dXrukO48XKSX7CtLYkLWXQs2N0+emvjWKlhFH462nN+xMx+gmbM05WFzablVMZfZyPIJdtXBOsz7VYn9tQmoHkLlP+xvpAlhHIhznguM8ZMFH4JoLejqggHs+eFaBKcH/d9hFRM3/n7xXkNYzEaaWyLxXKbWVWBBHHhbHOlk7RE4BbT8UvBXmpnxFmTFF15P5kP820rsOEfduBWwwOBWp9Ay7ZcuWvPHGG1VpS61g6j+f8/6OhaS6ssn1Oll4aBPX/P0W+wuPtrRShcJb/a7nto5jaB/VmDYRDRnXpFe5OqbbVDOjGndjUP1TuwhD6jnI9IvAvRB/SbkP3H/4u6mLCIRlEOj5+EMlLn/puZ7ij1eXax6ig+s3///1/lNB6wRYBoIoMVkRdjAnIOwTUKKmgGUoocMjbkL1iMT9N9KolDQog0rPsM866yz27y+9IKOmLna5XK5K2bbbncHq9B0BDXl1JE6fm5cSf+Cm+kMCju9JPB1ih/Ne+jJ+PrC2zPEjhZUp9UfQQW3Ali1bKmxfOCp7vyeTOOv31Lfno4iSM2Ud3ZdH2p63iDKvwGEOlkuVUkMikNICmFCEEyGCH5RSaqSlHSQzOYnW0ZFY1eywthzJ6pP4w1wpBXeQ7x1MlHkZMdY/AI1czwhyPcPhsD9v3KpOpGXUagTu4utLKQBZMqHo6J1JjbTkX8h2l9Zqo3Rq4+d8PJxq9wvVvOiYkFAzW1MlJSVVyra1u5ciDwVv14FtvvSQY9688j02ulPQytD5sygmrmo3jPPaDa+wXWVx5H51qZOYuZt9Bem0jmhAn/g2ATnhNQk9cy94gis3FcVNo7i94M0KGfUQAgQaOZ6hxDa+Bun8GVxzODbXWwgLDZtfTCNzAnrhLZD3dIjimKNjojRCibgZbGNpUZxu2A24GYAoIDB5MgHpbYvMewm8if63Aj2NcKEXRZhp3KQzTeyV/81U9ntdW6mr95uYmBh2n7GyVQFizHZMiopXC/7RRZmDY/m78g+xOedA2GKdI6gI6lujuLjlwCqz9VjS3Xncuup90ly5aFKiCkEjWyxv97+BeGsNbBSrNiO4lyL4c6Ob+//XnUro7BGJw7QRYR0M5u5I7xrQDlGcTy3sYDsHYe5S9OfF/iwR5+el2NMO7OcjC79Gun4B4UA4LgPbuGIxqmMR5k6I+Pf8FnmLSuZLa/prGxV+n4EBp1jhzPEyonHXkNttipnLWwWLGe0ryMBUivaySag0sERxXfuRfDb4/0I6/ari4XUz2V+Q6ZeN1b0Uah6SC9N5dEO4Eu+Th9QzwTaS0PMJE8JxOSLy9jD7/WjS/xASShSi3g8QeSeYe4HldIh+HpSW6IdPR0/tgcy4AMwdgdjwRlmH+Y/Lfw18/4J3JTJnGjJnavnUGU3tCP9z8+eBC3FqLeAbVJzjmmE3b96cb76peT/46iLS5O+KPnXt5wgEutTRkZzZpDsTmvcNOr5VRP2QXW7Arxz484j7q9tkAHI0Jxty9gWFZXxSZ23WbrI9hcRaggtKTjRSS0Pm3AOetYAKwuQXWxJHtFB0iH4OYWrrPz72Hci+PnggYSfLfS52qSNdc6HgQ9D2gogGx3Bw/QruRRTPuH2bIfcR/zVDZphY/ZKqWiqBoRWnX3zKuwGKimGklua/ltoCoTY6apKwIKOmQe7jBFZOmiH2FRRr8PfHwOBYjJDIMSQXZJDlyaddVGMiTMGiSf3rtWfeyGksTdtCntdJ33rtaFUipa8kbSIb0i22BRuy9uItsVBpU83c2P7Evf4W6h5MQsUbIn6qCoUCn+ukO2wpdWTmlaAlczTlDcAGETcizN3A0g8hSuQ4y1wQ8SAzizao/v/YJpCXORiZMRF8JSoVZQHkv1U0fqhZsUZR33n8jtkKKIi4t5B5zxNS80S6kO5FYO6MzLkfXAuK+k16kNZhiNgXi2fOiuMipNoImT/d79SVeH9jBNd8pIgEy6Aau6ZgUDMwHHYRh1w5TF37ObvzD2NSFHy6zjVth3F9uzOCfkR2k6XcVYgv9pnEk/9+x9K0LahCQRGCm9qfybnNT6uO2whJA1NU2NCMVTHT2B57wmwJi+dv0A8TMuXNOQdsYwKcte78DXL+S+BsVYBlEErMUzTIusM/cw4ifNPlYsxdEdahfmdqG4dQ4pB5r4Q5WAVhReY+Dq4/8He0KVosdS9B5jyIiH35qIXW08Ey0F/x6F1XJEqFPy5uGYiMfQ+lFrZ8MzgxGA4bfzHM7as+5IAzE03quIveiD/dtYRGttiQ4Y7yEmGy8lzvK8jzOsnxFtLIFnPCu5ubhMIdncbxUtKcgB6VNsXMnZ3Hh5WcPaH4dkEIaVgAtO3I9AuRanNE3Nt+0aj8FwgWZfKB52/0tLOIte6upCESZEFRjPwownEpMncHwZ3XVX9Tg4yLCZ6Bu/2zZz0bocQe3eyaA55/jhnLC56/IP1MZP0fAo83MCiiBvxSTz7/ZO0h3Z0bJJ3q0r3M2LWoSq4RZbbT3FHvhDvrI5zXoh9P97qcztFNiTLZ6BLdjOd6X8HZNaWi0tQWwjQa9uMEbScy8yp03QfavjDHeUHbEzLXuXyo/sXJY7FfCJb+wJHQkQmwQdSdCBFB2J+SMIGWFrBJFv5AsOMvQj+IzH2iUpYb1H2MGTaQ4swKuy/ddbyCQDWHoQ07M7Rh52q9htQy/M1o3X+CiEVETALr6LJjs5ZBfolTbT/hy8T9zQmEdylSxIEM9bkdZ/9GYUVE3Bg4onsZMv8Vf99IJQZMff2qgvYJCFM7f79JIcJkGGpFKYrltVGC67egnpYGBmDMsAHoENUYPUxqVrgFRYNgpHYImX42FMzwx2a9K/1pb3nPlHmuEAoi/gswnwaUomQnff7WWxHXAsemwSmUqpZXFqYuiPjP/SGXInTnfGTWrf5MEFlQVP6+BoQNUdSCTAgLRNwQWKoOfvsck4IkXYXjfPwLmuHQKFes3eCUw3DYQMfopiTENMdyzGKPVTFzW8ezTpJVtQ+Z/6Y/c4MSFYrSCYUz/T0Oy0CoDVHqfYZosBhM3cMdhFTbgzySggf+F0UrqG0p1dmXihVRb6Y/G6UIXcuE3GkEx8qdkD8dqR8tghERt0PE7UeVBEUkRN4IkXei57+NfmgAemon9LRxSKLBHOb+AEwdArNhDAyKMBx2Ea/0vZrRTXpgUUyYhEojWwyP97i4XI0NDIpw/0HomaHwL6gVIaUX6ZyLnn03es5jSG9gkwCh1kNEP0CwTKnZ75QLPoaCN4AjDtMHuP3pdGqrytkuVHD9XvynXvgjpA3zN/oNebwJfEe7BwkhUCJvQjRchWi4HNFwNUrk/0Heo5D/dlH4Rvp7VObcDY7rwHYhwT9BGyL6kcrdg0GdxwiSFeEwWXm0+8VM63oBTs1LlMl2QnJi3ZqXn/cnMi9lHSahcm7z0zirac+akblRYcK95guklgOetUhTG8i83p8VQiGgIJ3fIyNvR4m8+egZln4Q9zoy90nQUgDhbydmvwyyridk2y7fJvy52JVAOotywEH3bofchwh4Uwg63udP+zv2ToUKIsZ/iHYInLNDjOOC/BcQ9ecilVhwzvL3f1TbQ8wTRkcag7AYDvsYzIrphGVyuDUvN658lz35acXpdkm5+1mQuoEX+0xCqW1O23Ex5L9DsDN1QcE7yMIPQLrxL7odmYnr/v35byJt4xGmFsVnCesIqD/crxktrP5qwYJPkaUKaVWsF+ZRbEilOTJ7apFYVGnjKGBqizC1BkD6diML3gPPejC1RETciLD0BV8SCMvRvOwAM3cjs272x8OPZIxoeyDvKWT8F0ZHGoOQ1DKPULeYe2BtgLMGcGpeEjN3sypj50m0rHKIiOvB3BXEkUW2kl1hXH7Hi5fQYRMd6Zzl73Reckwh/HogRxyYEuMPR1Q5Lij8zF+2XpazVpsh4qYDIL0b/Bojzh9B2wHuRcjMa9ELvwOlYSlj2f0qfgHpfU5/mMVVyW7xBnUew2GfROanbghw1kdwah4WpZbW/LVmIoQVEf8FIvZNcNwItnFFzrs8qXZeKPgAeXgIev57SC0j9GHWMyl/JojA/xU3FdnhKOVcWRRSKSUMgvAvhsZ/i1Cb+s/KedTfPKHYMRc1VMh7Cqm2BaUZoeLUmFoWnXesGU6/JKyBQQgMh30SCRd6EYha29NRCAVhPR0leirCnBA6HBAWH8gMyH8RmTYUPWcaUgbOxoUSgYh9B0QEgTP4UNgg+nFEo3WIhmsQsS+AZTjh49yla5b7nfpWSB+J9KxGSqc/7BESgfBtRMR/CGob/wNDRAJWsJ0J5p6EfXiI0lL+DE5laqdXqCOc1/w01mftxakFOjWrYmJc094nyaoqxNSpSAgpVAiktL6LAD5wzkGKOET01IA9wjoAGi5HOuf55U711DBjeUBteTScYhsNMh/pWUHlY90uf/V61q3guLWUe9D9udpqE6j/i1+ESjvkbyOmNkN6EpGun4ObJggHwj6xkrYZ1HWMGfZJZGSjrpzeoDN21VL08i6wKmYubTWILjHNT7Z5x49lMKhNCZ4J28BxAyhl3aMLnF8gQ2iMCGFHcVyAaLAQop/zj1li5lxcB5V1M3rWzf5qREBaRhIywwSKsjvKOYeRuVDwfCkHRIKpqEGCEAhzd4TtTERR1aOw9AX7JQTmjQtQ2yItI8pnQxWQnlNA4vb9pGTmnrBrGlQeY4Z9ElGEwlM9L2Vd1h4WHdqESaic1bQnnaKbnmzTqgQhFIj/ApnzcFEzXQlqc0T0owjrEKS5PTL3sdCx3CNIj38WKkJ3xRFCQTjOR1qH+DupF34MaEVaIkUd0t3LkfnvIqL+g/AmIrER0mmrTf3Vit6NIMxFbwYeyg6VhCD26bCdaIptt45EFn5V8mbBtwPyn4ZqzsX2+jQe++x3/li7HYtZxePV6NepBc/dcDYRNiNDpaZizLBPMkIIese34e6Ec7ij87g646yPIJRYlLg3EI3+QTRcidLgd4S1qFmxbWxROXcpi4hKTFG8uozrqA0Q1kEQskLQDc4v/f9XSyasA/ZtBxSIuAXi3kM0XAGWAWVeOxgzwly2qJa/ZD9EjnbhN/5GCNXIS98uZuE/O/D4NPKdHjw+jdVbk3nwo1+r9boGx4fhsA1OCEJYEErUMdtsiPiZYOpK6K+iHSLvLH8Bk54DMjjrxr+vqCrS1KGUtEAveFdDwXuQ+yggEVEPleuBcRQVLAOC7vVYpJQBlZIBCIt/ll9NuL0+flq+Cbc3cG3B49NYkbSX9JxS+k4anFQMh21wUhGmVij1v4f6C8F2Gf7UOxMo9SB6Gorj0nKP5c/hDpOVckS7wzKoSD2vtGigE3z7kIVfIcwdIPZ1yl1BKaIRMaXFtosOEyJsmAd0fzeaaiK3MEwMHzCbVA5n51fbtQ2OD8NhG1QJeVn5/P3zGv5Z+C+ar+IZGIqpKUrsE4hGiX49jgbLK+SsAXD9EH6fxd/hx68K+DlYR+BfDA33E3CD66eicyIJ1jUJg3UMQm1QvmPtlxJczi9AqQ/m8nU0qgxxkQ7MptAPIJ+m0aJhbLVd2+D4MBYdDY6br1/4iU8f/RqTxeRfV7SoPPHDfXQ7PaHCY/m1OMLNPMtAO1DKzqOOWShxiLjpSL0Qmf8WFH5IyLi2byt62jiIug+EXo76HzuYO5XbXBF1F1LbBe6/QRRJw4poRNyH1apjY1IVbhw/gLd/Xo7LczQsYrOYuGBIN6LsRh54TcVw2AbHxep5//D5E7PwuLx4XEfjx9POfoYv975DZGxF4r/HiblP6AYIwoEwdw06XCgOcFyELPyMsKl+2k7IngKOS6Hw6/DHAQgzwn5euc0VwoKIexfp2+GPWSuN/PHvE6Ahc9WoPphUhffnriDf5cFqNnHlqD7cOL70RdYD6Tm4vT5aN4pHUYyGwScaw2EbHBffvDgbV0FwN3FdkyyauYwJt4w5YbaIyJuR7t+OSRM0g4hFFv6AzH8DzH0QEdcVi0wJU1tk5M2Q/y7+noyhptEu8G5ExL2OzH8bfHv9bwF6Jv6Hg+5PV4x9tczFxpB2m9qDqX3Fb/g4EEJw+cjeXDq8F4VuD3arGVUJ/6DYeTCd+z+Yy4H0XBQhsFvNPDJpNMO6tz2BVhtU2mHrus5jjz3G1q1bsVgsPPXUU7RqVUktYoNaS/r+zJDb3YVu0g+E3lddCFNbiP8cmfsE0rPe32LL1M3fPd2zAH+e83ak6weI/xJh9he2KJG3I60jkXn/A88KQoZHvJsQ1hF+BcEipNRB2w1YAlQGK4O/sEf1h4ROIIoiiCwjBJLvdHP9S9+QV+gufpw5PV4e+GAuM+69lE4tGla/oQbAcSw6LliwAI/Hw9dff80999zDc889V5V2GdQSug3tjKIGf43sUTYSBnQ44fYIczeUet+wLfs7aLgGtK0Ezpx9IAv9BTsB53VBRNxA+J+EJ1jXRCgIU7vjctbSvRI9/WzkoR7IQz3Rcx5A6jUrS2Pemq14fVrQu4fHq/HJ72tOik2nKpV22ImJiQwdOhSAXr16sXFj7VOXMzh+Ln/gAqyOwMo4s8VEo1YN6Deu18kxCgAV4fuXsF9x74bicvViLIMIrzFiBs/KKrQPpGc9MuvGooKdopRE5xxk5jX+PO0awu6UDJyeYD0YXUp2pYRRVTSoFiodEsnPzycy8uhqvqqq+Hw+TKajQyYlhVMyO7m4XK4aa1t1UN33O+XT6/nuuV/YuWYPJrOJvmd35/ypY9m2LUxhyAnA5XKxZ89BmkdqhHgBQErB1i3bODa/umOsghDBTlvTFVKTk8j3Vl1+dPPIZ3CYXAQmhHjQvdvZv+M7nL7ghdLSqK7POVLxYTWruL2B/y6KgEZR1iq/Zp7Tw6GcQhpE24lxhA/XnGq/YzgOhx0ZGUlBwdGKKF3XA5w1QEJCxdO6TgRJSUk11rbqoLrvNyEhgVHnjai28StDUlISrTtMQKb9D/RjFPFQEbYRJCR0CzpPz+gL3lVB21VFo3mb88qfY10O9EN7Q65xKkKnVdNCRETFPrPq+pxbt23Ptyt34vW50EvM/C1mE1MuGUXbJvWq5Dpen8ZTXyzgtzVbsZhUPD6Nod3b8MTksdgtwVK6dfV3nJiYGHZfpUMiffr0YcmSJQCsW7eOjh2NZrUGNQshVH8zBRFBceGLcIDSEBH9eOhzoqcV6ZuU/GnYwXFVlTprANRGobcLM6hNqvZax4Hdaubj+y6jW+vGmFUFi0mlWf0YXrvt/Cpz1uDXN/k9cZtf38Tl1zf5c/0uHvjA6MBzhErPsEePHs2yZcu47LLLkFLyzDPPVKVdBgZVgrD0gQYLkc6fwLcfYekOtrGIME0ChLkLxH+LzH8dvGtBqedvfWY7t+pti7wFmf0AgW3ChF/AqkQ2Sk2gRYNYPr7vMrLynXh9Gg1iIqq0uMflCa1vouk6f/27m9d++IspFwytsuvVVirtsBVF4YknnqhKWwwMqgWhxCEiJpf/eHMHRNwb1WfQkevYxiEjd0P+2/5ZNToo9RFx7yBEWd10Tg5xkfZqGTc730lp/v+rhf8wvEdberVrVi3Xry0YhTMGBicRJfI2pGNSUaVjNJi6VGtZek2lXrSj1MpJj0/j+7/+NRz2yTbAoG6QfjCTeR8t5MCOVLoM6MCoq4bhiKqe2VhdQyhRYB10ss04qZhNKteM7se7c/9G10OnNOYUlCILcIpgOGyD42b94k08dM6z6JqOx+Vl6Xcr+OyJWby58lkatqzihTqDOssN4/qz/UAaC9ZuD9pnt5gY0bNd2HM37Ull8YadmFSVs07rRKtGcdVp6knDcNgGx4WmaTx16csBeiKuAjcel5dXb3mfZ36ZdhKtM6hNCCF4avJYdqVkkHw4G6/mlwiwmFQaxUczrn9wCt+hrDwe+eQ3Nuw6iMeroagKM35bzY3jB3DtWf3ILXRjs5iwmuuGq6sbd2Fw0ti2ZhduZ3DTAF3TSVywHp/Xh6mO/FgMqh+L2cSn913Op/PXMHfVFqSUjO/fmatHn4bNcvR75NN03vl9A39v+x2fflT7RdN0NE3n3Tl/89Wif8gpcCGE4MzeHfjv5WeUqZtS0zF+SQbHheb1hV8kk4SNRxoYhMNhs3D9uAG0aVyPrfsP0zAuWAHx/V9WsnJHaoCzLolX08nIPara+Mc/29mfns3HUy+r1Yu6hsM2OC469Q8vC5owsCMWa+npaVtX72DLqh3EN4lj4Dl9MFvMZB3O4Y8vlpBxMIuugzsxaMJpqGE6pBicWDxeHz+v2MzsvzchhGDCwC6cO6hr2A42lSEtJ5/J/5tJToGLQrcXu8XE6z/8xbt3TqRDswas2ZbMZwvW4PGVv5u9x6ex40AGm/YeolvrxlVm64nGcNgGx4XZYuaeD27lf9e8idfjQ9d0zBYTZpuZKW/fGPY8t9PNg+c8y9ZVO9A1HZNZxWQ1M/mJy3jv3k/Rdf8C5tx359OwVQNeW/okETEnsBmCQRBeTePmV79l6/604k412/an8cvKJN6962JMoURbKsFTXyzgcHY+WtHb2RHhqSlv/YiUfmlXVwgxqrKRbN+fZjhsg1ObYRMH0axDE354bS4HdqSSMLAjF04ZT/1m4cuWZzw8k6S/txV3qfG4vJDn4o3b36ekUJ0z38WB7Sl88MAXTHn7puq+lZBIqYE30d953dIHocScFDtONgvX7mDbgfQAZ+ny+NiyP41F63Ywuu/xy1O4vT7+3rS32FmXJD23MMQZwQhCt6EQQtC0fu3+7AyHbVAltOvZmns/ur3cx//6wR8BLcWOEEpV1OfxsfDLpSfFYfslUG/Gr6ktQHqRkf+HEnnzCbflZPN74lac7uDPzOn2Mj9xW5U4bE3TkWU3zwyJAKIjbIzs1Y5fV20JUBdUFEFcpJ1+HY+v0cTJxnDYBiccTdNw5lesCMJbxiuw5tNYMSeR5C0HaNaxKXHtjz98IvV8ZNa1II9pKFAwHWnqgLCdcdzXqE3YQijmgd9Rhkqb83h9OD0+oh3Wci/0OWwW2jWpx7YD6RWyLcpu5bKRvblx/ABMqkKLBrG8/8tKTIqCV9Np3TiOl285t9b3oTQctsEJZffGfTxw1lNhX1tDIYSgz+geYfen7c/gztMfIi8rH3ehB6vDgsVu5s0Vz9G49XG0r3LNAxliYUs6kQUfnHIO+9zBXflz/U6cnsBZts1i4tzBR7W7nW4vz3+9kHmrtyKlJC7Kwd0XDWPMaUc7yv+5ficfzVvFoaw8urZuzC3nDKJjc3+R1bQrzuTmV2cF6W+riggZKunToRkf3H1JwLZrz+rPpcN7sf1gOnGRdlo2rBuFNNXfntnAoAjNp3H/6CfITMkKme5ni7DSfWgCthKi9SazCUe0nVtevDrsuM9e9RrpBzJx5rnQNR1nnovc9HyevvzV4zNYP0ygkl7JfanHN3YtpH+nFpwzMAGbxYQQIESRsx7UldM6Ni8+bsr0H5m3eisen4ZX0zmcnc9jn/7Okn93ATDjt1VM++gXNu5JJS2ngMUbdjL5hZms23kAgC6tGtEgJjKkGJTVrB7zt4lBCa34e/NevFqgg3fYLPRs27TOOGswZtgGJ5C1f/yLuzC4yAZANan8580bGH31cNYu2MC3r8whY38mPUd25eJ7z6Vhi/ohz8tJz2XLyu3oWuBMWOqSnev2kH4go9TFz1Ixd/drY8tjF7sUMPet3Ji1GCEE/718FOcN7sr8tdsRwJl9OtCl1dGsi23709i4JxWPL9B5urw+3vxpGX3aN+O9uSsCZs9S+hcvn/96EV9Nu4ol/+4iM68waD1D0yVtm8SRne8kt9BNhFUl1+nl46K+kiZV4bXbzqdH25qjJV7VGA7bAAApJX99t4I5786nMM/JsIkDOefmMVUq4JR9KCegY0lJzFYTY64ZAUDf0T3pO7pnucZ05rtCNgEGUE0KhXnHIRhkGQJqS/DtAko8aIQNEXlr5cet5XRp1TjASZdkx8F0lDDx6n2Hsti4JxWzGtxuDPzO3qtpbNh1kMIQi5sAOw9m8Pfr/2Hhuh089slv+DQdn3b0s7n9je/5/bmbsJeR/38sBS4PTreXetGOGl1YYzhsAwBeuPYt/vpuRbEmyO5/9zH33QVMX/NcleU/dx7QPmgmfISOp4UX9imNhi3rExHtCDlzt9gtNOtQ+ZxbIRSI/xKZ9zw4ZwNuMPdBRD+EMLWt9Li1lT2pmRS6PbRvWh9LGLmBZvXCp83Vj4kg0m4N+9A2qSqqUIrDIeH6EC/ZsItP56/B7Qt2+gUuD8Puns7gLq2466JhtG5ceg/OjNwCHvv0d1Zt2YcQgvgoB/+9/AyGdq+Zn6/hsA3YumYnS75dgbvwqICTx+kh/UAG3770M8MuHkR0/WjqNSk9FqjrOrNenM2sl34mNz2Pph0ac+NzVzHk/P4AtOjUjAHje7Pql38C9EesDis3PHdVpWxXFIU7pt/Is1e9FuC0zTYz/3njelT1+CrwhBKJiHkSYp5ESlmjZ1/VxZ7UTO5592dSMnJRVQWQ3HXRcC48vXvQsT3aNiE+yoHLk0PJZQqbxcT1YwfQtVUjoh22oBm02aQy9rROKIpgfP/OvPTt4rD2pGTlkVlKTram6yzdtJu1Ow5wyfCezFu9lQKXm74dmvN/559OmyInruk617/0DQczcvEVTSRSs/K4//25vH3nRfRs27QC/0onBmPR0YBVv6zF6wqeoXpcXr54+numnP4Qk9reztQzHyc7LSfsOG9N+YjPnviWnLRcpJQc2JbCs1e+xpJv/y4+ZtqXd3L2zaOJjIvAbDHRdXAn/jf/YRIGdKi0/UPO78/zvz/CaWf1pEGLevQZ3YNb353EiEuHVHrMUJyKztrj9XH9y9+w51AmLq+PApeHApeXF2f9yYqkvQHHZuUVcv1L33A4Ox9/sp8/rmwxqVw9+jTOH9KVvYeyuOKM3kTaLDisZkyqgs1iomFsBK0bx7MiaS8xEXa6tg7d71KXEgXo1a5pqR1qpIRCl4dPf19DSmYuuYVu/tywk0nPfcnu1EwAVmzeS3pOQbGzPoLL6+PdOSsq/W9WnRgz7BpIZmoWezYm07BlfZp3rP6nvNliQlEVdD34FVNKibMoDrzxryQeOOsp3k78H1JKEudvYMm3f2Myqww4uw+/frgQ7zHFMG6nh/emfsbQiwaSlpzOExe/xO6Nyf5SdIuJEZcNocugTkHXPRa3082Cz5aw9MdVRMY4GH/jmfQ+4+gMr+vgTjz760PFfyclJVX2n8OgBIvW78Tt8QWFJ1weHx/NW0W/Ti3YmpwGSJ758g+2HUgPcICKEFw3tj+TzuzL7W98zz87DmJSFTRdp350BMN7tGXemq1k5Tl5d87fmFR/SGTqJcO56+3ZxRKrJXnr5+W8PeUi/tywM2Qs/AgS0EoYfmRx8+3Zy/nfTeewMyUjaHH0CDsPViwP/ERhOOwahObTePmmd1j01TIsNjM+j492vVrzxE/3E1M/utquO+ziQXz2xCwo5csP4PNqHNiewpaV2/nquR/4549/cRW4EULw24w/kWGCjmn7M3AWuLh7+KOk7c/wNzooypb74IEvaNC8XnHYJBTOfCf/GfQgh3YfxlUUtlkxJ5FzbzuLG5+fVLmbNigXBzNyghrjHmHHwQzGPPAebo8Pn6aHdH4en8bMRf+wPz2HtdsP4PFpHImGpGbl8dPyTTg93uL8ao9PY396Np//sZbOLRry757g9Eldl2zee4hHJw7gx7XJrNm+v9yqkLqUrN6WDECz+jFYTGrQDBugeYPYco13ojFCIjWIjx/9msXfLMfr9lKQU4jb6WHbmp08esH/qvW6Tds15tqnr8Bqt5SpiicUwR9f/lXsrME/C/e6vfjCVCNabGY2/pVEbmZe0KKju9DN509+W+o1v39tLik7U4udNfibJPz45jz2bTlQnls0qCTtmtYPK/6fW+AiK89JodsbdqYKkF3g4vc1W4OO8Wk6+S5PUDGMpksStx8gz+UmFG6vj9TMXFrWj+KqM/syuEsrKlLAWOj2IqVkWI+2RNgsQVktNouJG8cPKP+AJxDDYdcA1i3ayIPnPMPXz/8YlO3g82rsWLub/dtTqtWGiXedw/TE/3Hpfedx/n/G0aBF6NxlXZNsW7MzoMNMaVjtFs65eQypu9PQwshhpuw+VOoYf3z+V0jdEa/by3ev/Bx2Zm9w/Azp2pr6MRFBSnyqEKXGkEvSKC50EUxpKELQND70W6UAsvKcfPDHRu5/fy5LN+4pXuAUAhxWE5ZSJh5SSjbsTsGsqnx4zyW0b+Z/KDlsFiJsFqZeMoKBCa0ASMvOZ2vy4aDqzpOFERI5yXz36hxmPDQzIEPjWEwWE2nJ6TTvUL0FAS07N+Papy4HoMewLjx/zZsBdpmtJtr3ak12Wm7YMRxRdnRdR1EVfB4fp43rRdchHdmyamfYH21hrpM/v1nGiEtCLxKKMNMnqUt++3gRqknljrfCS7kaVB5VUfjonkt54vP5LN+8BwE0io8iPtLBht1lTyJsFhN3nHc6L8z6s9R487GYVYU12/eH3CeBOSs3gwyWNzApCiN7tueei0cw7sH3cXuCr2lSBLtTMunZtinNG8Qy88Gr2J+WTb7LQ7sm9TCbVLLynfz3w7ms23EQs0lF13WuGzuA68b2O6mLz8flsOfPn8+8efN46aWXqsqeU4q8rHw+mvZlyNljSTwuL627nliVsaEXDSQ/p4AP7v8cd6EHXZcMmtCXm1+8mms6/CfseS6nm8atGjLwnL50HtCBN25/n3/m/4suJZ4QrcTA73hfmDyd3md0DxmrP2vySD557JuQ52tenXkzFnHmpOF0GXj8anEGwcRHO3j1tvNwery4PT5iImzM+G01G/ekhs2pFkC96Aj+c8HpjBuQgMvr44VZfwZIs9osJuIi7aRk5gWdX+j2lOoYw71UeTWd7QfSiY2007xeLDtTMoKOURSFZsfIrB4bs/6/N75ne9EC6pFQzofzVhIXZQ+ZzniiqLTDfuqpp1i6dCkJCcGNMQ3Kx4bFmzFZTKU6bIvdzKgrhhLXKPbEGVbEuOtGMeaaEWQczCIyNgJHlJ0VcxKx2C34vKE1NnSfzsGdqXz/2twKXUtRBEu/X8nZN41GSsnGpVv46/sVqCaVIef3p2nbRuzZlBzyXK/Ly+JvlhsOu4IcSM+hwOWhTZN4zOXIV7dbzNiLFPsuOL07H/y6MmQjAbMqmDT6NG4/d0ix073g9O44rGbemr2cgxm51I+J4Pqx/Xn9x7/CXC200FN58MfFdW46eyCPfvpbkI2qotC9lCYGW5IPszs1Mzjdz+Pjw19X1k6H3adPH84880y+/vrrqrTnlMJit5R5TO8zup804X4AVVUDdDzM1uqJomk+v+Sqrus8N+l1/p69xh+OEYKf3/6NLoM6sXdzctiZlRHHLj/JadlMfW8Oew9loSoCRVGYevFwJgzqWvbJRcRF2vno3ku55vmZAaJLAoiw27hyVN+gGfJZ/TpzVr/OAdvCFcgoigBdUhmffTgrj6nvzeGlmyewdvt+vl68PmC/2+vjvg/m8vrt54c8P/lwNqoSennPn2N+lH2Hs8jKd9KxWYMKl8NXhjJ/fbNmzeKTTz4J2PbMM88wfvx4Vq5cWeq5NTUX1uVy1QjbrI39sbHSiGsVzbbt247rOlV5v5aGCnooydHjRYH4DtF889YPLPtxFR5n0VuHlLgLPWxYshnFpKKFioMKaNWvacA91pTP+ERSnnv2+nSmfPwnuU5PwMPv6S8X4M7LomuYxeZwvH7tcD7/K4nVOw8hJfRu04Arh3YmNXkP5dEz7NI8nvV70kJI7UpURQkrZVAaPl3y96Y9/PDHchK37gna7/FpLN+0h3e+m8+whGbBoRdnHl5f6IynBtF2kpKSSM9z8vLPa0nJLkBV/HnlF/Rvx7mVlFgoL2U67IsvvpiLL764UoPX1HBJUlJSjbHt8e/v47/jng75xbRH2Rh4Zr/jtrWq7/e/n97B05e/iq7p+CqwkASA8EumAsVpgLYIK8MmDuKMCcN5aMKzR511CTSfhinMyn+n09ox/vIxAT+8mvQZnyjKc8/zE7fh1WTQm4rHp/P7phQmjjm9wtcd0Ld8Ql2huMsaw7UvfhPwhqQIwQ3jB9KzbVMenvErGXnOCr9BeXwau7N9JGcUhNyvS8mMRUkkHSrgpZvPDciCSQDe/H0TyWnZAedYTCpTLhpBp04dmfrIR6Rm5Rflf/t/uz+t2U2vzh04q1/ZhWClkZiYGHafkdZ3kulzZg9eXPRYsRM7gmpWiW8cx8Bzao6Mp6ZpTL9zBk9f/iqqSUXTdH/utrn8eh0Wq5nL/3sBY68bSfOOTeg8oANT3r6Jez+6DSB8PF9Cn9E9sEfasNjMCEWgqApdBnfi1aVPnZJl45Vhf3p22EKY5FJkByqC0+1l7fb9bE0+XKajfe3HpcEbBeTkOxnQuSXznr2JT++7jFG922OuQJPfI1rd8aWoTXo1jTVbk/0ZJyVYuWUfaceEPo6MOaRra1Zt3Ud2vjOoWMfl8fH+r9Vb0m6k9dUAup+ewMtLnuCN2z9g57rdKKrC4PP7c8dbN5RZyHIi+fSxb/iluBej37Fquk7Lzs3IScshMzX4By+EPy1RURU0r4aiKHz3yhy8Hh8X3DGeG569MsDZjrxsCEkrtgXledsirJz/f+N4aOZdLP9pDXmZ+XQflkC7nq2r85brHG2b1MNqNoWUL23ftPRwiKbrLNu0h4X/bMdqNnHOwC50bxOYajrzz394/Yel/nCGlMRHOXjllnNp3yxYz/xAeg4bdqYEZZroumTWkg3cddFwTKpC19aNeeGmCei6ZP2uA9zx5o8UhJFfPYIiBMO6tyU+0sEbPy0N22Xd6fHx3ZINnD+4W/G2T35fgyvEQ00RgvmJ25AQNjvmUFawo69KjsthDxgwgAEDamZFUG0jYUAHpq95Ho/bi6oqFXLUXo+XP2cuZ/Gs5dgibYy99gz6ju5R7lnn4eR0vn91Dv8uSaJRm4ZMvOucIH0Pzafxw+u/BOWL+9w+DmxP4ZPtb7B19U7euuMj0g5koJpUhBC0TGiOrmns3eRfMCwZQpn91jza9WzNGZcffQ0fddUwvnnhJ/ZvC8zxVU0qXYZ0wh5pZ9SVQ8v9b2MQyJCubYiPcuD25gZkYdjMJm46e2DY83yazh1v/cD6XSk43V4UIfh5xWYuHdGLKRf4P49lG3fz+g+BzvGAO4cbX5nFr8/ciM0S6G5SMnPxhVnD8Wk6mXmFNIyNLN6mKIKm9WJKrao8eqzCdS9+jSIEETZLWIcNBDnngxmh3zScHh+pWXkM6doGQejfVpvGcSTtO0S0wxaUOlgVGDPsGoalgivNHpeHu4c/wt7N+4tnpSvnJDL66uHlKibZuzmZOwY/iMflwefR2L52F6t+Wcvtr13HuOtHFR9XkFuIzx36S2+2mjm0N51mHZpww/NXEdcwGkesg29f+Jm/56wJ22XGVeBm1os/BThspCQjJSvkfX7x5Lfc9L/wrcIMysakKnx076U8+ulvrNmajBCCetEO/nv5qKDZcknmrkxi3c6DxY5PlxKXx8fMhf+QX+gm1+lm857UkI7R69NYtG4H4/oHZohEO2yl2pqd72THwXRmzFvFgYxcElo05MazB9KnY3NWJe0L2xNUCIqduoYku8CFIkTIWbEiYEzfjqTl5JOV56RFw1i6t2nC/vScoJCHw2qmc4uGdG/TmHZN67F1fxreEg8Pk6qw40A6N73yLT5Np03jeF68+RyalqIRXlEMh13L+eWDP9izKTnAKboK3Pz+yWLGXncGHfuWvmr95n8+xJnnLF6EkhLchR7emjKDEZcNwR7h/1FFxDiwRlhDdi93Oz18OO0Ltq3eiWJS8Hp86D69XCv8u9bv5aFzn2PSwxPp1K89a35bH/LNwOv28duMPyvssHes283S7/zZTKdfNID2vdpU6Py6SP2YCN76z4XkO924PL5ydVn5afnGkM7Y7dP4YfnGUsWXCt1eViTtDXLYzcuYgb41exkrk/YVO9/UzDyW/LubZ68fj8vtZcOulCCnHa7xQbgQhi5hwdrtfPjrKswmFU3XOW9wN6wmU0A5uklVqB8TwdDubRFCMP2OC3n2q4Us+Gc7Ukqi7FbynG5cXq1YRG3b/jSuf+kbfn7y+qDS/spiLDrWcuZ/tjjkDNbj8rD0+9LTLnVdZ/3izSG/4CaTyqZlW4v/VlWVKx68EGuJBrng1wpp2KIeW1btwO304Mxz4XP7yp2OpeuSVXMTuWfko6z5fT2uAlfYhapwlZJH2Ja4k08f+5ovnv6OQ7vTePvuj7lzyEN89dwPfPXs99x5+kNMv3OGkbNdRKTdSv2YiHKFzkIp2h2hPEp581ZvYd7qLQHb3F5f2HZiAH/9uzso/KHpOo98PI8P7r6EPm0bYlIEqhCYVQWLScFUiYYVOw6k4/FpFLg8uDw+flq+kUtG9KRr68YIITCpCqN6tefjqZcVO95Iu5WnrxvHXy/fxoLnb6ZpveigfyNdSvKdHv7evKfCNoXDmGHXcsJ94YUQpf4QD+5MJT+7wL8YGEIH2+vxBml4TLxrArpP56tnfyhOyRtzzQjmzViEt4xFoNI4Mqt/4/b3efHPx/GF0H8QQtD7zNAVZlJKXr7hbRZ9vRyPy4OiKEf08wPytt2FHn798A8Gn9ePXiO7hRzLIDTj+yew42B6qbHg0vBqOi9/u4Qxff1dZQASt+/HZgm9AFoaLq+PV79fwr/7MvAVPSw0rfIP4WPPdHl8/LpqC/OevRGvpqEIEbaQxmI2YTGbOJgRWl/H69PYX0XZN2DMsGs9YyaPDJr1gn+B5vQLgxeED+5M5ebe93JTj3uYOupxkBJFDXbsHpeXjx/+Cm+J10IhBJfedz7fHv6Qj7e/wfcZM7jumSvQtQrmYofhcHIGFquZifecgy3i6D2pJhV7lI2b/hda+3r5T6v585vluAvdSF2i+TQ0rxayyMZd6GbeRwurxN5TifOHdKN1o/ighcOKkFvoIiv/aGsvu9VS6XTMeauD5VoBVEWgVkRrNQxpOf5sD7OqhnXWJWnbJHSGjUlVaFtG9k1FMBx2LWfsdSNpmdAsaLsuJd++Midgm8/r4+7hj7D73324nR4Kc51oPh09zOxkz8ZklswKzis1mU3UbxqPxWYhIsaBGkYvuTJY7BauffJyHvjsDrqd3plmHZow9rozeHfdi2G77/zy/oJyy71KCa6C4+ikfoohpSQ731+4MmPqpdx36UgGdG7J0G5tiLCFllYI54M1XWd+4jbSc/zFLP07taiUw1YUEVAOH3BtBB2aNQhy2mZVQRECs+moyyvNsTcJI+0ajlsmDMJ2zO/ApCo0iY+mX8eqE24zQiK1HLPFTOPWDdmxdldALFr36Sz9fiV7px2VqFwxJ5HCPCeynAINrgI3C79aWmoa3YEdqejlSLMqC9Ws0ndMz+JFziHn9y+1C01JnPnld8C2SCvDLh5cKRtPNf7evJdnv/qDQ1l5SGBQl1Y8etWY4pzlZZv2MPW9n/H6tIAUwUiblQKXJ2R+9es/LuW1H/5iyoVDad0onk7N65O4vWJNKBxWC6d3a8O81VuCtEZMJoWHrhxFw9golm7czbJNu0nPLaRn2yZccHp3flu9lZ+Wb8Sr6ZzRqz07DqSzcU9qwGzdZjFx27kV+4707dCcZ64fx/NfLyKrqDJzcNfWPDJpTHEIqCowHHYdYP2fm0IuHApgw5+baD+iJQApuw4H9VwsC2sZAlVbVm7HbDWXWaIuFIGqKmg+HZPVhObTUFUFn1dDNanoms66hRt56NznuPH5q2iV0LzcNg6dOJBtiTuDFl+FIlDNanE6otVhoXXXlgybGD7f2MDPpj2p3PPu7ICY9d+b93LdS1/z3aPXoCoKQ7q25rMHruCml2f5Z+FFx+U73SFT7iQUj/fCN3+iClEcgw6FIgQdmtVnx8F0FEVBQRBhN/PcDWezbudBlGO0RqwmlX6dWtCllV+J7/wh3Th/SOBaxU1nDwzIN3e6vTz95QIWrN2OEAKr2cTt5w1mfP+KyxqM6Nme4T3akZlXiN1ixhHmDeR4MBx2HcARbSc3I1hTWDGpRMYdLTxo3a1FWOcqFBE087ZFWBl73RmlXju2YUy5Xmt7Du9KrzO6smTWCvZt2e8vxZd+BXpd86cAugvdrJqbyIbFm5i+5n/lbtgw9rozmPPO76TuSSvOJLHYzCQM6sjpFwxg/qd+Rbgx1wxn3PWjgmQADIJ5b+4K3McsMPo0nfScApZv2sPQ7m0Bf7Wi2+sLcNDleX+TEnxlZOtYzCoPXH4Gu1My+HXVFmIi7fTv1IIpb/2ELvWQWRmXjuhVjqsfxW4189S143jwijPJLXRRLzq4u05F8Oe1R1T6/LIwvrl1gPNuH8vHj8wMmmHqmsaAc/qwN3kPAH1H96Bes3hSdx0KcNpWh4UBZ/dl5dxEPC5/vzubw8qISwbTb2yvUq/d+4xuWB0WCvNC62MfYf3iTXjcXg7sSCnKAjl6fVkihn4kY+TzJ7/lgU/DN0ooiT3Cxpsrn2X29N9Y+OVSVLNKn3O6MnnaFZjMJs7/v3HlGsfAz5EWWqHcqdvrY+fBjGKHvWZrcoWzPMpCEQKLWeW8QV15adZidqZkFFdXLli7Pex5Xk3nvvfm8PtzN4Wc3Xo1jQ9+Wck3i9eT73TTsXkD7r5oOH07NsduNZ8QedTjxXDYdYAL7hjPxmVbWPPbOnxeDc2nFc1cJTf3uIfLnzmfhIQEFEXhlSVP8NL1b7Pm9/UIAfGN4/jPWzcwYHwftq7ZyeJvlqFrkmETB5IwsGOZs2fVpPL8/Ee4f8yTuPJcOMMs6Eldsnn51pD7jkXXdNb/uYmswzl888JP/D17DfZIG+fedhZjJo9ADZFra4+0c+l953PpfecDfuU6YyZdcaSUPPzxPPIKQ3+OVrOJpiW6AsVFObCY1HKVi5eHaIeVsf06M75/Aonb9/Pj8k3FYlXhil+O5c8NO0OGNB788FeW/Lur2NakfYe55bVvef328xnUpTUAWXmFfP3nOlZuTaZRbCSXj+xNz3ahF7tPBsY3ug6gmlQe+24qK+as4fGJLxW/k3rdXlL3pDH9hk8YMLwf9ZrEEdsghidnP4Az34mr0IPZYiLjYCaFeU7a9WxFVmoWP7/zO89NeoNWXVtwxbQLSRjQodTr12sSx1UPTyRpxTaW/bgaZxmz7fIQGevg5p73kJdVUJzzPf3OGaz5fT0Pf333cY9fV3F5fMxduZmF63YQ47Bx0dAe9O1Y/vWAjXtSWbhuR9jGATaLmRE9jlbPju/fmffmVo1CndVs4qbxA7liVB8AHvlkXlhlwXBouk5eiP6o+w5nseTfnXiOaQSt6ZJ73/2ZJa/czqGsfK569oviLvBCwJJ/dzHlgqEVDrVUF4bDrkMkzt8QsopP8+n8+sECrnr4qK65ajbx0bSP+ePLvzCZTXicHqSUAYs4KbsOsXb+ev77xRROvyC0yNe8jxfx2i3vIQT4PFqVVBHaIqzUb16P/dtSip01+LNWVs5dy9Y1O2neoTE/v/07f32/Ake0g3NuHsOwiQNPaZlVp8fHFc9+QWpmLi6PDwEs3rCTK87ow+3nhW5wfCxLNuwKil0fwWLydxm3lHhzaRQXxVOTx/Lwx/P8fTsrOdO2W0xE2q2898sK3py9jCi7lbSc0FrWpSElbD+QxiVPfkqk3cqlw3sx5rSObNpzKOxDyOnxsXTjbuauSCK30F08k5fS/wB89fsljO/fmagytE9OBIbDrkPs3ZQcsljE5/GxZ1NgB+rXb3ufRTOX4XV5S80c8bi8PDHxJe7+4BbGXhu4APnCdW/x+8d/HpfNqklBAja7FSklPq/G2OvOYNUvawOc9RG8bi8rfl7Dgs+XkJmSVayfvWXldlb/upZ7P7r9uOypzcxdu5uD6TnFTlPid0af/7GWCYO60rJhbJljmE0qihK6n2KnFg1o1SguaPuoPh0YkNCS2X9v5pXvFleoF6OqCBJaNSIn30VqZi7eoglDZSoqVUXg0zR+WLaxOGtqa/JhVmzZy7h+ndFK6e60ass+lm7aHTLsYlJVVm1JZlSf0t80TwRG4UwdokPfdphCVKKZrSY69DkqepSXlc+ir5aWqc1xBCklL93wNrf0ncry2avJOpzDQ+c+e9zOGsAaYeOHzI+5/7P/cMf0G/l42+vc/tp12CNDz2ZMFhNbVu0go4SzBv/s+89vlrPjn93HbVNtZfnWlJAzXF3qLNmws1xjnHVap5B6HDaLiQtKaT4babdyxRm9ufD07gHVkKFeeFRF0DA2ksFdWtGvYwu2JaeRnJZd7KxLw2JSGdqtDd1aNyY+0krz+jFE2a0I4Y9x6zJQ/Mnp8TFv9VZiI+1hKxaFgNhIe6m6JlUl3nS8GDPsE8iWVdt5995P2bp6B45oBxNuGcOVD11UZYtj5/3fWH5++7eAmemRBgIlpVKTtx0sl2BPABJ2/rOHR8//H4oiKn5+GNyFbhyRdgaf2y9g+4Rbz+Ltuz8J0t9G+svrQ70VeN0+Vv6ylva9T01FvnD+RiDC7zyGVo3iuOnsAbw3dyU+zV8QY7ea6d2+GecM6FLm+Q9cdgZdWjXi8z/WkplXSKTNSmZeIW6vD7Oq0KFZA26dMIgurRpx4eOfkJ3vrNCM3GJSefnWc1EVpbgl2pXPfkHSvsNhz9F1nZVb9tE4Lor96SGabACdWjTkjF7tmbdma3C6oC7pn9Cy3DZWJ4bDPkFsXbOTe894vNgB5aTl8s2Ls9m5fg9P/Hh/ucY4sCOFRTOX4SpwM/DsPnQd0jkgZtuwRX1eWPgYL173Fge2pyAltOneknFTRjBvxkIObE+lY9+2/PDmryHDDeWlws5aEFTkcISmbRuFPGXs9Wew+rd1rPltPV6Xp+jNQXD3B7cw64XZIc9RVaXCeuJ1iaGdmzE7cRfuEGGxM3qVvznstWf1Z2i3tvyyKgmn28vwnu3o36ll2Iq9vEIXv67ewr7D2XRq3oCzTvNneVz+zOf+mXPRQp+Ukv3pOXRq0ZDvl24k3+mpkLMGf6HLqKnv4PT4sJsVzh9ymO0H0ks9R1EUCpzuYn2QY9ElPPDBXKSU2C1mvJqGy+PDrPrDQ09OPgu7pWZ8rwyHfYL4aNoXQbNFj9PD2vkb2LMpmdZdS9cb+P71uXz43y/9wkY+jZ/e/JW+o3vw8Kx7AtLcOp3Wjvc3vEzW4RwURXBgewr3jX4CqUs8Li/zPzWF1LSuSlSzCtLfpQYA6f+xKuoxlWkOC9c+fUXoMVSVR7+9l62rd5A4fwOOKDvDLh5EvSZxFGQX8t59nwX9ewpFMOziQeWy0e1089Uz3/PrR4vwuDz0H9eba5+6nMatG1bupmsA43q3ZsOBbPYdzi7OW7aYVG4YP6DCIvrtm9XnjgvK7uyzNfkwN74yC5+m4/L4sFvNvPHTMq4b24+UzLxiZw3+jIwCl5tZS9azbufBCmeAAGhSklv0uXt9Gp8uWFvmORLJzpSMkA+yIxyJmQshOLN3BxRF0Cg2ivOGdK3SBgTHi+GwTxBbVu0IvUMIklZsK9VhH9iRwocPfBEUs02cv4EFny3hrMkjg86JaxiDrus8PvGlgIIab5iuMVWFavGrmx3bTFfq0t8x3WJCCEFkrIMbnr+KoSEUBY8ghKBz/w507h+42DP+xlEsn72aTcu34sp3oZpVVJPKjc9fSaNWDcq0Udd1po56nJ3r9hTb+efMZayet473NrxE/abxlbjzk4/VrPLpfZfzxz/b+XPDTmIcNs4b3I0urUK/xRwvUkqmvjeH/BJrIU63F7fXx0fzVuEMUVDj9mos37SHNo3rhe0Co4ZZ9AyHIHx1pcWkcuUZffhyYdmOHfyOe9XWZOY9W3a3ppOB4bBPENH1oijMDc5PVk0KcY1iSz138TfLQ4YTXAVu5r43P6TDBtjxz+5K50RHxUVQkFNY4fCHI8pepN0R/GOVUtKsfWOe/mUaDZrX8+tWVwKT2cQzv0xj3cKNrJybiCPawagrh4ZV8zuWxPkb2L0xOeChousSZ76Tb174idteubZSdtUEzCaVsf06M7Zf57IPPk52p2aSkRuceqfrkoycQkyqErLxQb3oCC4d0ZN5a7YEZYOYTQq3TRhM347NmTL9J5wuL66iRgfhCmckR2RVFTw+DVXxa8GfN6gL148byMvfLS51dn0s6ZVIJzxRGA77BDHx7nN4//7gsIjZaua0s3qWeq6r0I0vTH5ruH6J4E/nO7YJQXkpyHUyPfF5HjnvfxzeV3qMsCS6T8dbyqtuyu7DLPthFRdOObtC9njcXhZ/vZylP64kMiaCcTeMos+ZPehzZo8KjQOwYclmXCEU/nwejcT5Gyo83qmK2+sLG9dWinSpj/3a2iwmLh/Zm04tGjL1khH87+s/izMwNE3noavOLK5S/PXpG1i4bge7UjL5699dbN2fFtaW07u1oXOLhmzae4i2TeK5ZHjP4lBGVgUnLU3qVUxa9URiOOwTxIRbz2LX+r0s+HxJcVaI1WHh2XkPlZklMmB8X3547ZcgzWeLzczwS8LHbDv0bRu2kEQoAovVjLuU1L5WXVrwxE/3cUvv+0q17wiKIug3rjd7Nu5jz8bkkMd4nB4WfLa4Qg7bWeDiztMf4uCOVFwFboQQLJ71NxPvOYfJj19W7nGOENcgBovNHBS2AYhtUHN/rDUNv+506LckXcLgLq1ZvnlP8TE+TefG8QOKKy8vGNKd0X06snLLPn9HofZN2Xsoi6R9h+jcoiEWs6n4TaF7m8bc995c3L7gyYDVbOKKM/rQr1PosOKwHm3YtCc1qDt6KEyqwu0VlFY9kdSM5MJTAEVRuOu9W5ix5TXueu9mHv1+Kl/tf5d2PVuXeW6XQR3pN7Z3QBcWi81MvabxnHf72LDnmS1m7nr3Zsw2c/FM22RWsUfaeGnhY9zy8jUh87aFEPQY3gWT2cQ3YTIygs/x/1e9xrEc2J5S+rEVDIX88Pov7N+WUvzAklLiLnQz68WfObCj9GuFYuTlQ0I+yGwRVi64Y3yFxztVMakKD115JjaziWP/NaWULN+8lyFdW/PwlaN54LIzmPv09Vx7VqDGeaTdyqjeHShwupnw0Ef8580fueHlWYyf9gGb96YWH3d6tzacO7hLUNMBVVG4bESvsM4a/A+G2Eh7QC61EATZrCiCuycOPyHhpMpSqRl2Xl4eU6dOJT8/H6/XywMPPEDv3r2r2rY6ScOWDWjYsuyFsZIIIXhw5p0s/HIpc9+bj6vAzbCLB3HebWcREVO6lOPwSwbjVp0k/rCJA9sPkjCwIxfddQ7Lf1rFR9O+QjUp+EpMsi02Mxa7hSnT/Ysum//eFnZse5SdiBg7GQeykFIiNZ3Z038rNQvFbDMxZvKICt3/gs+WhCzy0TWd5T+u5uJ7z63QeHGNYnlw5l08ffmrKKooaiumM+HWs8rdNMHAz5l9OtK0XjS3vPod+a7Az8jt9bF04x7unji81EyLdTsP8OzMhQHxbKfby82vfscvT19PlMOGEIL/Xj6Ki4b2YM6KzexJzSTWKrj+3OEhqy9LEmm38sW0K/ngl5XMX7sNVRGM759A4/goflmZhMvjY3jPtlw1qi+R9uB2ezWJSjnsGTNmMHDgQCZPnsyuXbu45557+OGHH6raNoMSqKrK6EnDGT1peIXPbdGlKWMuOlo4s/q3dcx4cGZQOEQ1KUy8+xwumHI2sQ38P7CGLeuTujt0UcI5N4/mpzd/DdAPKStlsF6T+IAinuOlstolgyacxjcp77Ny7lrchW76jO5Bwxb1q8yuU4kurRqHlVg1m1SS9h0u1WF/8vuakPolmqbz7MyFSOlv2XXB6d38kqgT/b+BpKSkMp31EeIi7Uy9ZARTLxkRsP3iYaWvH9U0KuWwJ0+ejMXi15vVNA2rtWY/lQwC+fr5H3GFUDQzW800adeE3Ix8lv+4msi4CC6ccjZbV+8MrjgEFny2uGI53QIuuffcChe3nDlpGF889V3QLFtRFYZcUPkZsSPKzsjLyieKZFA6MRE2svKDF/d0KWkQExnijKMkp+WETMtzeX3MT9yGpktMqsLMRf/w5LVjGdX75Gt6nCzKdNizZs3ik08+Cdj2zDPP0KNHD9LS0pg6dSrTpk0LeW5SUlLVWFnFuFyuGmtbdXDs/e7feTD0cQVuvnz+W9L3ZoIQKKo/Par/eT1ZOnN10Gw261BwmW+pSPjwoS8xxyu06lF+yc8uY9pR/5M40pOz8Dg9CCEwW02MvGYQud5scpOyg+/lFPuM4eTds6brNI4JdthCQIzdjMmVRVKIz+gILeJs7EklpJrekXxsn+bvMPPwjF+pb3JjMamn5GcsZCXfKbdu3crdd9/Nfffdx/Dhwa/piYmJ9O3b97gNrA6OaBCcKhx7v89e9Rp/zlwWlGNttpqQUNwD8QiOKDtulyekEmBYSqlmsEfZ+XTHG8VhF/Cn2v364R8U5jg5/aIBjLh0MOYS5cDFaX0/rCQy1p/W121I+MWhU+0zhqq/56x8J699v4T5a7ejaTqDu7bmnonDaVY/MLzx5Ofz+XXVlqAsjHrRDj6573KalpEmt/dQFlc8+0XIQptjibBZeOa6cQzt3rbOfsal+c5KhUR27NjBlClTePXVV+ncueauqBqE5ooHL2L5T6sD0gRNFhNSlyH7Peq67m+gWxGHXco0wOfx8tuMRcXdYd6//zN+eus3PE43UsLaPzbww2tzeeWvJ7EWLQJZrGZGXz2c0VdXPIZvUHHcXh/XPP8VqVl5xcUvSzbsYu32A3z/6DXERzsAyMwtZO7KpJAqgYoQNImPIt/pJt/poUFsRMg0wFaN4nj3zok88+UfbD+QhhACTddDNpaGSmjZ1CEqldb30ksv4fF4ePrpp5k0aRK33nprVdtlUI20SmjOC388Sqf+7RFCYLKYGH7J4LCSprouw/54KoPX7WPflgMA7N64j+9emYu70F18DVeBm71JB5g9/beA83Iz8/jruxVFvSfLJw1rUDnmr91GRl5hQKWiLiUuj5eZf/5TvG3HwXQs5mA5VoD03ALufmc2o+57lwse+5jR97/Hz39vCnlst9aN+XLalSx55XaWvfp/jOzZPijtDvyhkdNKSeGr61Rqhv32229XtR0GJ5jO/Tvw5opn0XwaQhEoisLjF73Ish9Xhcy8uOius5n5/I/la4mNP34ZzsnbIqx07Otv4vrG/31wVCSqBB6nh/mfLubie/wpe7Nems3HD8/0FxmJot6DX99Nv7FGOml1kLhtf8gQhcensWprMrcV/d04PipA4KkkAsHyTXuKda7dXh/PzlxItMPG8J6h1QOPqOL1bNeUhesC9XeEgHsmDiMiRIPdUwWjcOYURzWpxZoek5+6DFuENaCoxGI30753axxRDhpUIO3NbDNjiwzOHhJCYLFZOHPScFyFbjYvD5/nfeTBsW7RRj559Bs8Li+FeU4Kc50481w8PvElMlKyym2TQflpFBeFOYRovxDQOC6q+O/m9WNpWi8qaDZsKZImPbYpgcvjY/rPy0u9dla+k+mzlwVtN6kqOWGaA58qGA67FlOQW8gvH/zBp499w98/r0HTjq9zdauE5ryx4hkGnXsajhg7sQ2jsdgs7N6wj48fmUlOWm7QOaEqBi02M537d+DLve9w0V3nEBEbgaIqqCaVLoM68vrfTxMR7SAtOR2TJfTrNMDAc/wLL9+9MidkWqGu6Sz4fMlx3LFBOM4b3DVkvNlqNnH5Gf63mkKXh0nPf0lqZn7Ai5dJUejSuhFmU+jPNjktu9Rr/7luR8juL16fxo9LN5b7HuoihpZILWXLqu3cP+ZJdE3HVeDGHmmjYcv6vPLXk0TFlZ73WhqxDWMozHXic/tw5bsDVAKP5EErqoLVbkHzaTTv1JRJj17MD6/+wua/t2GLsDLuhlFc8/glWO1WbnnpGm556RpyM/JQTUpAZWZ841h0LUzcRMAFRXoj6QcyQx7idXtJ359R6Xs1CE+T+GievWE8D370a/FD2adpTLlwKD3b+lURp/+8nJ0HM4IWHC1mlVsnDOaut38KOXbJGXoo3D4trDKfx6dxID2HF775k2WbdqMo8xnRsx33Xjy8zHzvuoDhsGshmqbxyHnPB8i1OvNdHNiRyvQ7Z3D/J/+p9NgPnfMsO/7ZHTJb5AiKSeGhr++iZULzYsH/088Pr2sNfnnZY4mIiWD4JYNYMuvvACEm1awy8rIhxBfJzvYc2ZU9m5KDuuTYI210H1r30rpqCsN7tGPB/25h9dZ9eDWdfp1aEFWidHvOis0hs0OEEBS6PTSpF82e1MwAbWubxcTNZ5feZGJwl9a8+n3wm5NJVRjctTVXPfcleUXdzTVdY+E/21m/8yDfP3oNjjoe3zZCIrWQpBXbQ1Yq+jw+Fn+zvNLl2rv/3cvujcmlOmsApKRe0/gq6c4y5e0biW8SXF489tqjGt8T756AzWENkIo1WUzUb16Pwef1CzrXoOqwWUwM7d6WM3q1D3DWQHiNaSlxuX28ePMEGsdFIYRfWMlqVrltwmDO6tep1Gu2bBjLxKE9AtpyWUwqsRE2YiNsON3egBm4pkvyCt38unpL5W+0lmA47FqIM98VVjbV59Uq7bBTdh1GDRN3DLiGR6NJu4p3Mdm1YS/fvzqXeTMWkZ/tF4n/4/O/yD6mYlLzajx6wQu4nf6HUv2m8by56lkGTTgNi92CI8rOWZNH8vryp6usgbFBxenfuUXI3r5eTadD8/rc9tp3pOcWIOXR3OmUzLxyjX3PxOE8c904BnRuSecWDZk85jS+efhqNu89HHJW7/R4WZG077jupzZgfNtrIV0GdQw7C04Y0KHSnVxadmmOVh7NYIuJ/KwCHJH2co2raRrPXvk6K+asQdd0VJPKm//5kIe/uZvvXp0T8m1B13X+nr2GEZf6tT6atW/C4z+UT5fb4MRw14XDWLv9AC6PtzjsYbOYmHRmX35avon03EK8JZyr26vx/dJ/uXhYD1o3Lr0NmxCC4T3bBaX/NakXFbb7zN+b95CeU0D9MhQsazPGDLsWEhHt4LqnL8fqOPqKqqgKtggbt79+HQAbl23hrmEPMyF6Eo+NeZnZb/9W5sy7eYcm9BjRFYutdHEm1aRWSOj/l/f/YMWcRNyFHrxuH64CN+5CN09e8jI5aaFnXJpXIztEVopBzaF143i+fugqzh/SjZYN4+jToRnPXjeeWycM5o9/tgc46yPoUmfpxt2VvuZlI3uHTDcEf5736z8urfTYtQFjhl1LuejOc2iZ0JxvXviJw/vS6TKoI1dMu5AWnZqxfvEmHhz/TLF8qivfxXtTP2Nf0n7+7/XrQ453aG8ab/zfB6z5bR1Sl8XxYnlMGbDVYWHCrWOwVGBx58c3fg2ZlieEX741LzM/6GEiFFGqVohBzaBpvRgevOLMoO2mME5VEUrYdL/y0LlFQy44vTsz/1wXtE/TJQv/2c4T15xV6fFrOobDrsX0O6sX/c7qFbT9nbs/DtK6dhe6+eX9P7hi2oXENw5c5CvIKeD/+j9AbmZ+sYOWUuKItjNgXB+W/bgK1WxC82qMv+FMbnj2ygrZWZhbGHK7z6vR58zu7N+egrvAVVwZabVb6DWyG+17t6nQdQxqDucP7sa7c1fgPibEJpGc0av9cY3dt0NzZv+9KawGd13GCInUQXau3xtyu9lqYsuqHUHb581YhLPAFdiZXfpV+1p3a8HXB9/n9eVPM+vQB9z26rXlWpgsyWln9UQJMeNSTQojLz+d15c9xWlje2OPtFGvSRyX/fcCHvt+aoWuYVCzuPyM3nRu0QBHkfa5SVWwmk3cM3E4DWKPL196QELLgFTBI6iKYORxPgxqOsYMuw5ij7QF5GgfQeoyZOx549ItIbuve1xeNixJ4oppFxEZW/mFnKsevpilP6yiMNdZ/FCwOqz0H9eb9r38s+hn5obWVDeonVjNJj645xKWb9rD0o17iImwcvaALuXuEFMakXYr/738DJ75cgGaLtF0ic1iIspuZcoFQ6vA+pqL4bDrIOfcPJof35wX0KFFCIiuH0XCwI5Bxzdp2wiTWQ3KPFFUhabtGiGlDJtGWB4atWrAO2tf4LMnZrHmt3U4ou2cd/tYzrllTKXHNKj5qIrC0O5tGdq9bZWPfe6grlh9BSQm53IoK58BnVty7uCuNb4n4/FiOOw6yDVPXMaeTftZv2gjQhFIJJExETzzy4MhHe+EW8Ywe/q84FRBAb99vIg5784nYUAHbnv1Wjr1q9wrZ6NWDbj3w9vKPtDAoJy0rB/FWUNPrabJhsOug1isZp6e8192b9zHtjU7KfDlc96141HV0LHnJm0b8fDXd/PsVa8XZ2u48v2qaB6nf2Fn89/b+M/A/zLg7L7c+L9JtOzc7MTcjIGBQTGGw67DtOnWkjbdWpKUlBTWWR9hwNl9mXXoAzb/vY0da3cz45GZuAsCU/GkhBVzE1m3aCMv/PEonfuHboYqpWRb4i5SdqbSqktz2nRvVWX3ZGBwKmM4bINizBYzPYd3ZeuqHUF9HYuR/o4wb/7nQ95c+VzQ7uy0HP479mn2bzuIUAS6ptOpX3uenP0AjqjyVUYaGBiExkjrMwiiXtP4MqsdtyfuwusJzoN9+rJX2bNxH64CN848F+5CD0krtvHqze9Wl7kGBqcMhsM2CGLIBf3LzLVWVCUotzr9QAablm8NWrz0un389f1KPvjvFzx87nN89OCXpBk61gYGFcZw2AZB2BxWnp//MLGNYgjVCdVkVhlywYCguHh2Wi5ma+gom8/j49uXfmbFnES+fflnru9yJ5tXhG8PZmBgEIzhsA1C0rFvO2buf5e73rkZq8NaLDRlj7LRqHVD/vNmsCZJ845Ng5oMlORIs12v24cz38Vzk14P0BDxeX1sWbWd7Wt3oeuhG7saGJzKGIuOBmFRVZXxN57JiMuG8OfXy0lLTqd97zYMPKdvUMjEVejm8YteCNkBPRyZB7NI3X2YJm0bsezHVbx4/XR0TUfqEkeUnYe+udsQgDIwKIHhsA3KxBFlZ/wNo0o9ZvqUj9iweDOarwIzY+FPAdy1YS/PXvVaQHm8M9/FtHFP88n2N4grahVmYHCqU6mQSGFhIbfeeitXXnklkydP5tChQ1Vtl0EtwuP2suCLvwL6MpaH+MZxNGnbiO9fnYM3RBqh5tP4bcaiqjLTwKDWUymH/c0339C1a1e++OILzj33XN5///2qtsugFuEqcAXpZpeGyWLCFmnjgc/+gxCC5K0HA5UCi/C4vCRvO1iVphoY1GoqFRKZPHkymuaPVR48eJDo6PJ3HzGoe0TFRRJdL5LMlOywx6gmBQm07tKCAWf34ZxbxtCwRX0AEgZ2YNuaXfiO0U62RVjpXEntEgODuoiQZfSNmjVrFp988knAtmeeeYYePXpw9dVXs23bNmbMmEFCQkLAMYmJiTgcjqq3uApwuVzYbLaTbcYJ40Tc7+o565n56Gy8JcIiFpuZLsM6EFUvksg4B/3O7UX9FsG9/DIPZvPs+W/iLiihLqgIImIdPDLvTmwRFVdgO9U+Yzj17rmu3m9hYSF9+/YNua9Mh10WO3fu5Oabb2bBggUB2xMTE8Ne9GSTlJQU9ICpy5yo+1324yo+nPYlB3emEt8olsv+ewETbhlTLmnWHf/s5pWb32Xnuj0AdB+WwN3v30KTNhXvzg6n3mcMp94919X7Lc13Viok8u6779KoUSPOP/98IiIiyhQWMjg1GHJ+f4acXzm5y/a92/DWqudw5jsRioLNUbd1jQ0MKkOlHPZFF13E/fffz3fffYemaTzzzDNVbZfBKYo90hCIMjAIR6Ucdv369fnwww+r2hYDAwMDg1IwStMNDAwMagmGwzYwMDCoJRgO28DAwKCWcNxpfeFITEysjmENDAwM6jzVlodtYGBgYHBiMEIiBgYGBrUEw2EbGBgY1BJOGYet6zqPPPIIl156KZMmTWLv3r0n26Rqx+v1MnXqVK644gomTpzIH3/8cbJNOiFkZGQwfPhwdu7cebJNOSG8++67XHrppVx44YXMmjXrZJtT7Xi9Xu655x4uu+wyrrjiilPmc4ZTyGEvWLAAj8fD119/zT333MNzzz13sk2qdmbPnk1sbCxffvklH3zwAU8++eTJNqna8Xq9PPLII3VSFCgUK1eu5J9//uGrr77is88+IzU19WSbVO0sXrwYn8/HzJkzuf3223n11VdPtkknjFPGYScmJjJ06FAAevXqxcaNG0+yRdXP2LFjmTJlCuDv7HIqaL48//zzXHbZZTRs2PBkm3JCWLp0KR07duT222/nlltuYcSIESfbpGqnTZs2aJqGruvk5+djMp06jbNOmTvNz88nMjKy+G9VVfH5fHX6w46IiAD8937HHXdw5513nlyDqpnvv/+e+Ph4hg4dynvvvXeyzTkhZGVlcfDgQd555x3279/Prbfeyrx588qlkFhbcTgcHDhwgHHjxpGVlcU777xzsk06YZwyM+zIyEgKCgqK/9Z1vU476yOkpKRw9dVXc9555zFhwoSTbU618t1337F8+XImTZpEUlIS999/P2lpaSfbrGolNjaW008/HYvFQtu2bbFarWRmZp5ss6qVjz/+mNNPP53ffvuNn376iQceeAC3232yzTohnDIOu0+fPixZsgSAdevW0bFjx5NsUfWTnp7Oddddx9SpU5k4ceLJNqfa+eKLL/j888/57LPPSEhI4Pnnn6dBgwYn26xqpW/fvvz1119IKTl06BBOp5PY2NiTbVa1Eh0dTVRUFAAxMTH4fL7iDlh1nbo/xSxi9OjRLFu2jMsuuwwp5SkhCfvOO++Qm5vL9OnTmT59OgDvv//+KbMgdyowcuRIVq9ezcSJE5FS8sgjj9T5tYrJkyczbdo0rrjiCrxeL3fddVeN7W5V1RiVjgYGBga1hFMmJGJgYGBQ2zEctoGBgUEtwXDYBgYGBrUEw2EbGBgY1BIMh21gYGBQSzActoGBgUEtwXDYBgYGBrUEw2EbGBgY1BL+H7mA82iKaAueAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data with k-means labels\n",
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(4, random_state=0)\n",
    "labels = kmeans.fit(X).predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assignment of points between them.\n",
    "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n",
    "For this, we must think about generalizing the model.\n",
    "\n",
    "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hypersphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n",
    "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n",
    "We can visualize this cluster model with the following function (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "deletable": true,
    "editable": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n",
    "    labels = kmeans.fit_predict(X)\n",
    "\n",
    "    # plot the input data\n",
    "    ax = ax or plt.gca()\n",
    "    ax.axis('equal')\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "\n",
    "    # plot the representation of the KMeans model\n",
    "    centers = kmeans.cluster_centers_\n",
    "    radii = [cdist(X[labels == i], [center]).max()\n",
    "             for i, center in enumerate(centers)]\n",
    "    for c, r in zip(centers, radii):\n",
    "        ax.add_patch(plt.Circle(c, r, ec='black', fc='lightgray',\n",
    "                                lw=3, alpha=0.5, zorder=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n",
    "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled, as you can see in the following figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(13)\n",
    "X_stretched = np.dot(X, rng.randn(2, 2))\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By eye, we recognize that these transformed clusters are noncircular, and thus circular clusters would be a poor fit.\n",
    "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n",
    "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n",
    "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual groups.\n",
    "\n",
    "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n",
    "\n",
    "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n",
    "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for noncircular clusters.\n",
    "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Generalizing E–M: Gaussian Mixture Models\n",
    "\n",
    "A Gaussian mixture model (GMM) attempts to find a mixture of multidimensional Gaussian probability distributions that best model any input dataset.\n",
    "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture\n",
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "But because a GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the `predict_proba` method.\n",
    "This returns a matrix of size `[n_samples, n_clusters]` which measures the probability that any point belongs to the given cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.    0.531 0.469 0.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [0.    1.    0.    0.   ]\n",
      " [0.    0.    0.    1.   ]]\n"
     ]
    }
   ],
   "source": [
    "probs = gmm.predict_proba(X)\n",
    "print(probs[:5].round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 50 * probs.max(1) ** 2  # square emphasizes differences\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach, which qualitatively does the following:\n",
    "\n",
    "1. Choose starting guesses for the location and shape.\n",
    "\n",
    "2. Repeat until converged:\n",
    "\n",
    "   1. *E-step*: For each point, find weights encoding the probability of membership in each cluster.\n",
    "   2. *M-step*: For each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights.\n",
    "\n",
    "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n",
    "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n",
    "\n",
    "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # Convert covariance to principal axes\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "    \n",
    "    # Draw the ellipse\n",
    "    for nsig in range(1, 4):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n",
    "                             angle, **kwargs))\n",
    "        \n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    labels = gmm.fit(X).predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        draw_ellipse(pos, covar, alpha=w * w_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With this in place, we can take a look at what the four-component GMM gives us for our initial data (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, random_state=42)\n",
    "plot_gmm(gmm, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters, as we can see in the following figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This makes clear that GMMs address the two main practical issues with *k*-means encountered before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Choosing the Covariance Type\n",
    "\n",
    "If you look at the details of the preceding fits, you will see that the `covariance_type` option was set differently within each.\n",
    "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n",
    "The default is `covariance_type=\"diag\"`, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n",
    "A slightly simpler and faster model is `covariance_type=\"spherical\"`, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n",
    "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use `covariance_type=\"full\"`, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n",
    "\n",
    "We can see a visual representation of these three choices for a single cluster within the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![(Covariance Type)](images/05.12-covariance-type.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Covariance-Type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Gaussian Mixture Models as Density Estimation\n",
    "\n",
    "Though the GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n",
    "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n",
    "\n",
    "As an example, consider some data generated from Scikit-Learn's `make_moons` function, introduced in [In Depth: K-Means Clustering](05.11-K-Means.ipynb) (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n",
    "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm2, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lQQAdmolowkRQlXPW9Ht4nGlOy8iPHDkSzz77LADguuuusx9fuHAhFi5c6HhtIBDAz372s9P5ugGDYbHTNvCZNEf1LuLU4vnhhQFohuVaHpmJLFFQSlCa5wOD6GBNyfjePW8cAookPidHxlWiBLGEhcKAKj4vWYrYFu809CsvHIlNR1p66Mt3xs5Tn7/qoipcP2uEo06ec47l51UCEIY+ZWDL8nxoiCQc+/3hoSbIlGDVxVXI88lZJan29yYHiHAutuHF7bUikZv8KCt5Z/3osLhxXj9rOF7a3Y4d9anvEy98d18jAOBzl4wGODCswA8GgkjCREw3keeTkeeT+30Yx2Nw4WWJzgCxhNUnBt4nSyjJU+3BFrkacBgTFTWAMPY90UNnDCgKqraB5xxJWQShQLnq4lH46Y3nQc7xWRbjUCWKSMJEJCE8Vt1iUBUKxjkoAUryVCyaWgYlI6ZNCbLi6opEcNn4kqxEckCVMao4iJI8FYVBBeX5fows8uPWS8fgH248H99ZPhWPfnpGloEHAN3ieO9AIzTDwovbTrhGjigBzh9VAJMxtMUN/O/HJ/DRoWbXaiLD4vjwUDOONsWw/aTm+n3v7Gu0G7hOtMZFcxhELqRdM1HfkUDCPPVSWQ+P3uJ1vJ4BFPnUPbW4YSKaEOV8KXwKRdgvozzsR2GA4bKqID6o0ZBIi9moMsVVk8vgVyS70iVXeaT9HongsvHFtuZNLoKqjCsmiI7VdJExVSKYP7EM+QEFlAq5AJqm524FOSKaMPo3JsMl7+5vhJT0umdX+pGfH8bbexpBqbjhXDFRhGJUmUJJCospMoXkUsQe9qsAdAAS/IqEunYt9yqHENR3aHjvQCPc9pRzYMHEUgAiPLblaEtWRVA6hAA1LXHkkuShhKA1ZmBYgYQOzURNSxwjkoJrgKguaozoyPPJyPd7Xr3Hmccz8meAoCrDDIoYdVfEDRMRzUJUN+BmazVTeITFQRVFIRW3zipGSRHDXz85KZqUOMeiKeVYM7cKpiVqvWVCMX9iGd7Z15Cl/phSZ5w3sQyfu7jKluZ1KAoQOOR7v7RgAgKqjDer60GIGA5y5aQy3LNgfM4VQ6qLNJ6UOrjlkircMHsEWuMGCgMKmuprMX70aHx+7mgkDCaEvwIKNMNCh2ZmedFuWjRhvwqfbCGWsLrUyEk9njseD/vYdyTMnJU7KTgHSvN8OVdqjHMUBjtFzKIJE8daYhhVFHTE5CMJEwnTQlFQ9couPc4onpE/Q+T7FQQUCRHNtAdHp0iYopEmnqMBSkxaElOVLM5xrCUmbgg6w22XjsFNF46yRcICiiSMYCz1t4yvXDkePpnijep621O+clIprjt/OErDPle99pxIQhLAYhxr99RDkgje3tsIWaK484qxOQ09IeIY5AdkxA0GxjiGFwYgUwLWLqMgzRCqsgRCCAKqDJ8sIZowEdMtmIzjqfcO4c20/Vg0tRxfuFx8rypLyf9RlId9ON6qObZBocDl40tRHvZ3cRMANh9twfxJpQj75JxNXwAgEWBaZT5CPhnji1UcbDEcXr9CRfVPZpVOXLdwtDmKquKQw9AbFkdjJIGSkM+TR/A4Y3hG/gyiSBRFIRVFEFUwHZphd6iyNNleZsv4wjbumbREO1cFAUXCiMIALMbx5PqDDmO+eGo57rxiLO6aNxa3zK1CS0RHQVCFX6bgEDeQmG51K7CV8vAJAX674TDW7W1w6Na8mRQqu2/RRKHbnja4Q6YkS2ssYTB0JAxX3ZqYbsKnpEI+BOGAgpBPxk9f2Y23dtc7RNRsLZp54+z3/8+HR9EQye46LQv7sfLCUZAowSVjS/Du/kbXfd1woAmLp5SDyyI+v+1YW1bIhgCYPrwACyaWAQBmV/rh9wXwyYk2e31gMI5E2g03Hc1gONocQ1Wx06NnHGiKJlCa5/M8eo8zgndVnQU452iP6zjZrsFkDEFVgipRey6pPZwaHOkh2oRhob5DQ8KwkDA7lQ+t5Hi+X79zEG9U10G3GLSkUuUb1fV44u39aIsbMEyGPL8MiwkJ4Fiqjd+00gaKsGSoJ2mqksM2FEnotFic463dDY48ACA6Wl/bVQdVJgj7ZQR9EnyKGM7hIiYJn0JRmudDUVBFptNKUyGjNDTTwmu76ly/983qensVFDcsvFld71DbTNEY0SFTDkUiWDSlHFJODXrg5R0nIVOCxVPKcf6oAiE/nJwTe8GoAnx94QRcNbncNtA0edIyFzIfH2vDHz866ro9mmHhWEus81infX9TRIfZRX7Ew6O3eJ78GcJMTmSK6gZqmuOIZYZmCKDIFAookDGHwmIcv9twGG/vbXDUiC+tEmEACoIO3cBrLrIFusXwzr4m3HnFOASTwlnCHqWNzEt+v5sxzqQ5lqzWcRM7IwQN7TpGl/b8MvIpFIUBCUVBFTHdRMJkCPqkrARkY0TPWVdOqRj0ESgMoCWqdynGpltAaViFT5FAKWDlKGz5+GgLVl80CpGEhc/MGolPnT8cEc1EfkCEkOI6w8k2DVHdREiVYVgcO2s7kLkwMRnHtmNtONwYxYSKcNZNIK5bON4ax8iigGOfLc7RrplZKwAPj9PFM/J9QGrUnsm4bdw5ONrjBhojerehEcY5LIvD5ELE63/eP4r3bA128d4NB5pgaAHMmi7c4J+9dThn/FiiBBHdRGGod1OM4rqFpqiOkpCKki7EzizOUdzL7/ApFH7Fh4BCwSDKTq2041Sap2Z5vCk4B8aXhUAJQVmeL6e4GGNAUdJoBpJNXuv3uYdsZIlCkSUUSBQJwwIg2bkLi3G8uuskPjjULBqtODAyLOeUbSAEaInpONkWR3nYnyWLEE2YON4Sx4gMQx83LJgW88YMevQpnpHvBamRe/b81AwrwxlQ16EhkshWZ+TJOLwYscdtGd8UmmGlGfhODIvjo5oY4rpwRd/NYawAYZT8ioRoQrw25bQTAnveqZsXbzGOJ9cdxKs76+zBIEunV2DJ9Aq8nhE68ckUy2cMQzjQSyMvS8jzyXbiNt+vIK5biKa8e1XGivMr8dK22qzvXXF+JQqCwniHAwpWzByGlz85mfW6hVPKHUnmO+eNw7v73EspUzcECuB4a8xRPfPidqFrbzFuLxhq2o0sLz4F50Bx0IeoZmFzczNK8nwYWRRw9ABEEiZqWzVUFvodhl73jLxHH+MZ+R7AuUg46haDYTIYSaMu5IJ1lIU756MmDIa6ds2uP7eShtxMJli7qsEGgLa40WX7/ZGmGBjnkCSSsxv1wrFFoERU8WjJRGBRMKVYaYESgnyfDJrhYT657iBe21XnSHS+tqsOi6eWY8m0Cry6q84eJXjtecPwd8smn8JRFMiUIqxKdmdrOgFVQkCVYDEOzbDw4FLx+S9tq7UHh6w4vxJfWzTR8b6vXz0JhBLH65ZOr8Bd88Yl59SK45Tnk7F0xjC8WV3nKC/NvCEUBnxoiYkJXAnTwoeHmrPOm8XFfZISOIy9TAlmjSzAG9Unsfloq30WKQEWTCrD6mTpKgC0awZIG1BZ2DmTwRs45dHXeEY+BylvPTV6j6cZXZMx/PNr+/DCthO2x/up84fj7vnj0BhJQE/eCEyLdVmSl4nFOEKK7AhbOLYpTdY3VwiFArjt0tGwGMfv3z+Ct/c02Nt45eQyfH7uaMgyTd5IOonrFl7dWec+Taq6Hn/44iW4/fIx6NBMVBUHkec/tUvHJ0nwqxQ+WUJdNzK+EiUI+WSEfDL+4bPn41vLpuBYcwz5AQUBl2HkMqX45tWT8aUF412HlrPkYHLT4vjqVeMhEYLXdtXZFUkLp4iyzBRFIQWRhAHDYmiPmyI34HK8ZYlgfGkI+xuidu7kglGF4AA2Z8g5MA6s29sAQpKyB0na4gYIIRhWIObG+rxSSo8+xjPyaTAmhlAkTKvLTtB/fm0fXtx2whEeeGHbCTRGNNx04Sj7x+02n9TxfZzDsoROfEw30BoTib6LRhdh05GWLAXG2ZV++3OunFyGdXsbHVUcikRw5eQyhHxysuzROa5v3d5GKJTi3kUTsralKZo7wSoRoVMzsSLc5RSlTCgh8Csitt0TqQXXz6AEZWE/ysJ+5/kxWdZKJqjKqCrOvqQpJVCpBFUGgj4Z3752Kr5+9UQ0dCRQktTktxi3tWsY56gqCeFESxwV+cSWJsiEc+D6WSMBAB2agbBfrE7+4bXdrtH6lMzzZ2ePdFwPrTEdlADjy/O8UI1HnzPkjXz6XNWuDHuKmG7ihQwDDwiP9939Tbju/OFQJIrnN9dkKSjeOGekGLtncnToOpojBkI+CW/sqsdHh1vsUMOFowsxp6oIm4+Kuaicc1w4phjLx3Qahs/PFd7gujRpgAWTS/H5uaOhGRbe3tPgOgrvjd31uHPe2KyRdV0lWBnnGFUS6JGBJxClhz6lcyZqX0EpsUM6gFjN6EmjLyZY9XzZFFRljC7pvPwzVYbz/Ao4F/Ny500s7Zwdm3o9AS4YVWg3MZXk+QAATcmBJ7lWYwBwojWOcWVO/fqEwaDpFvL9vctxeHjkYsga+dRsVc3ovjEonYY2PSvUkYImhzy/vadBVMNkVMcwBiyfOQwvbD1hG3XDYgBPvipppDYfbcWFo4vwf66dgva48O4L/CriLXX2d0mU4LbLxuDmi0Y5Yu4EBM0RPecMV4kQNEV1jFSds3kDqoSlMyrw2k5ngtUvU1x3/nBH+COTM2nYu0JyMfoJ04JhilCbyU4tXJZJediHaMLEqouqAMAhKzy5RMXSacOy3hP255ZYAIT3z5ioJgr6JPhkCUFVgiJR1LUnIEvUK6P06FOGnJHXTYa4biGRq2A6FxyI6RYkiXTp8fplmmbgOzEsjvcPNYlxccdaHQOqMzEsjk1HWrB0RgXKwsJDVGWKuMtrQ6qMgoAKmRDIEoEkEfgVmrOs0OIcJUkjQiC6UxWJQpUpvr18Cvyy5Mg1XHf+cHxjycSsz5GIEBBTpbNr2LtCokTcjNJspGj2Shr9VJlrDy2/JFFU5PtxvDWOz10yGp+dPdIeEHLoaI1rHb8qU1xQJcJtmRACTB0WBgjQkTBQFFKzEtAnWuOQJeJ59B59xpAx8hYTgmGnbNwhJHg7NAMW5/CrFEumVeC1XScdy/eUVK5mspzVMZxzbD7a2q1KZIojjTGMKQ3Cr0jIUyXEJSLi20QYZ+oiHwAkvfLpFVkdoz6Z4poZw+wW+mz5AYIHl03GVxeOz6oaoiR5M5AoFIkMmNixIlEoEhBAZzwmVcZqssz/ij6F9NMTDijIixuIJEz4FQnDCsTnhFRxQ3WTachVIsM5sKeuA7tf24NLxpbgMxeMgCwRhNJWSZwDR5tiGF+WlxVS8/DoDYPeyHPOEdUttCd64b1DLK3bNaNTUsDiuPb8SnQkDNeYu2GxnMt1kwGU9MzAGxbH/3x4zP7sv7t6MiIK7fEP/54F40Ep8MqOOjvW/6mkVy53E1wPqjLGlCi2tIEwlAPDqPcEklz1uEz7sxEaQsLg5/tk7K3vgGXBrrIKqRLKioM42aZ13ieJWClurWnL+bkpx+CDQ00AgBvnjMTwQj8CitPQH26KYlxZyHUkoYfHqdBrI88Yw/e//33s2bMHqqri0UcfxejRIhlYXV2Nxx57zH7t1q1b8ctf/hIzZ87E0qVLMWnSJADA4sWLcdttt53mLnS1jRytcQMmYz2eTpSJnqYZwyyOk+0aOOe4+aJR+PSs4VnVMxLtenzeqcSIU174xgNNeNJ/EMtGuxta4dlTUAJIVHjakkTwf66dhm9cPSnLK3cj1SSlpP47iIx6b6CUgCbNtypTjCkJ4USayqVfFlo8uskQ0zudh7a4AYmSbkNChsXxwaEmrDivEifaNIwo9MMvd54f0+I40hTDuNLQgFk1efRPem3k33jjDei6jmeeeQZbt27Fj3/8Y/zqV78CIAZxP/300wCAv/3tbygvL8f8+fOxYcMGrFixAt/97nf7Zuu7oS1p4E8Hv0JhMSF/W9uuOUbI+RUpqzQypluYN7EU7ZqBrcdye3TpUCK8N0UiWRrwgPD+Xt1Vh8Ujh8EnS90qPqaTWUUCJG8KqbBL8qbQH2Lq/ZmSPB86NBMdmpnxuIp4SxyabqFNM+CXaY8T+ZQQtGkGfIqE460aRhYGHJ57wmA4nDT03nxYj97SayO/efNmzJs3DwAwa9Ys7NixI+s1sVgMP//5z/H73/8eALBjxw7s3LkTn//851FcXIxHHnkE5eXlvd2ELkmYlt2ZeloQMYKuIaInR+HRLCkCQKwaWmIGNNMCCDB3XAl2nmh39eYpAJKU5+XguHxCCT49azgON8Xwb28fzCrPBEQnpcE5wqfYhERA7Bi6kvTUPYPRO0YWBbCvPuKIw8uU4sVtJ7B+X6eYXGmeD40u4wgzYZyjIJlg5Qw43iqmSKUb+rgulCurioPejdijV/TayEciEeTlddb6SpIE0zQhpy05n3/+eSxbtgzFxcUAgHHjxmHGjBm47LLL8MILL+DRRx91He5dXV3d282yMRlHe6JzGZ3QEti3b98pfw5jHA1RCwmXHyznooEmYTK0ahbMtJdYFs8psEUpcNsFhWAMGF2kwidTaC0NKGIMVo4bk2kxBImZcx8oIZCSKpNScgwfTcoG9zc0TeuTc3wuiOoMJzoM6IkEDh0+hOc/acXGY1GIqY3ifNe1aVBloKu5YBIBZpT70Nhw0vF47XGgLE/Jmot72CehPK9vU2gD+TykGAz7AJzZ/ej1VZOXl4doNGr/zRhzGHgAePHFFx1GfO7cuQgERH321Vdf7WrgARHu6Qviuhg/x8Gxb98+TJyYXQrYFcK7ikEqyr0i6IgbaI2bCLpE/S9uIdh0uDmrc/XCMcWYOGY4FEocuiUAsPAk8PbeBkcna6pWvShPwpTJk0CTYZr0kM1A8vKqq6v77ByfC463xrF5xx4MG16F9/9WCyPj8mAAMqI6IMRZdMM4QBQfyioqoWbE3GUJGFEYzMqLlBT4UB7299l+DPTzAAyOfQD6Zj82b97s+nivMzqzZ8/G+vXrAYjEaiqZmqKjowO6rqOystJ+7JFHHsGrr74KANi4cSOmT5/e26/vEQFVQklIJBzlUzSCnImaZc0ldJKiJaqjJW44dG3SWTGzEheOKRZhEolApsAFVUVYMVMcE7emqtsuG42FU8qgShQBhcIvU6y8cBT+v+tnCB32ZG11yCfDr4gmmoFk4AcDlfl+qJSgOZpb8z6TzDA9B7C9ph3PfHQ0a/VmWuLay8wn1bUlup0b7OGRSa89+auvvhrvvfceVq1aBc45HnvsMTz11FOoqqrCokWLcOjQIYwYMcLxngceeADf+c538Ic//AGBQACPPvroae9Ad1BKkOeTke+XUBryJTshhX4746mxe9m/wNq2OOKme8kl5xzHW+Ko60jYQyXckCnBp86vBOccmw63gFKKj4+2QJUIbpg9EoVBFWG/LAZ5kE6jf//iSbhn/niYjNszRT36D5QSVIRlmF1o3vcEk3Fsr2nD/IliiIiUVtpqWBy1bRpGFAYczsCxlhhU2auh9+g5vbYelFL84Ac/cDw2fvx4+98zZ87EE0884Xh+1KhRdtXNuYBSAj/N/nHwZD20xcSwj7p2DYTCnqyUjmEy/HLtAbyXViN/6bgS3DB7BKRk2CSl3U4IwR8/PIrNR1ocHa4fHGq256PmKlUMqBLGleZ5A577KX6ZoqQ0iCXTKvB6dfaYwp5CCNAWM+BTKMryfA5D3x4z0BTRMbkibBv1VA39hPK8IV/m6tEzPBcRwhhLySRlc1RHTLdcvXPT4vjZ2/uypjZtPNgEQoBVF1c5Xq8ZVk6Jgw0HmnDfVblzBHk+2TPw/ZzysB9fWyzO4WvVnVr7FWEfTrZr3VbXAMJoh3wyDJOjMZJAadgPcOBPW2rw0WHhSHAAS6cNw13zxoka/LQaeq9SyqM7PCOfRodmoL5Dc33OsjgON0bwzv7GnEb7+gtGwK9ItsRwoguJA0oIWjUdeQH3U1CaVDX06N+MKQnhy1eNx62XjkFzVEdxSIVECb72xy04ntY8FVQlJAwra8DIjOH59s1cNznq2zQ8/cFh1LYlkq8Sb3h1l6jCuWeBWC3HdQs1LXFUlQTP/E56DGg8I59EMyzUtuU28LVtcRxv0yCCMe5GuzmqY/3eBlvuwK2ePgXnQEnI3ZCHVNlVf96j/6HKFCMLgzjaHMOIpLLnv687gMaI7nidYTGU5/vR0JGwK21mDM/HlZOcfSJ/23EyzcCnv5/jtV11uPXSMXbopi1uoL5dQ3l+31XceAw+PCMP8QOsaYm7dioyxnG8NY7//uAI3tvfiFyhV8Y51u6uxweHmh2hnNSIuHRjr0gES6ZV5EyepZQn+yMW44jqJjgX3cCqV92DgqCCEl1FU0RHXLc6RyimYVgiHPOda6egpjmOoJIdjtNNhl217V18E0ddRxxjSjr7U+raE/CrkqdaOQhgjNsRAJ9MURhU+uS3NeSDvoxx1LRkl6ulnjvZpuG/PziCDQeachp4RSK4ZGxxmoHvhKNTssAni67T+RPL8OWrxrt+Vn/34pujOqIJEzHdRHNUR2NEh9mDYSuDncoCPwKq1GVZJSViYMzECveEejRhdjmYhXExJCVzIMmx5hg049TF9zz6D4bFUduuoUMzoZsMHZqJpqje/Rt7wJD25DkXXnrCpVSScyFG1qYZrsnTFIpEMKeqCDNHFODDwy1wC+WoMsU3l0yCT6YoCCgYVRTM2Ynan2Pxcd3KuhmajKExoqMgoAzpsj5CCKqKg2iLGTnLKlMyBj5ZQthvoUNzXnchn9zlIO+LxpSAEor6dg2VBZ1NdIwBR5pimFCe1y87nD26xmIcLXELhRk2JpawoPms03b6hrQn3xBJIKqb7s916EiYDG1xI+ckKIUS3HbpaCyeVoE8vwIrh0fLOEd52IeKfD9CqoyQz/2khVS5XxvKXN4iB0drXEcsx7EcKqgyxaRheVgyrSJrILdY7ZXAl/zBFgRVKDLJev+M4flJjSQnlQV+fHa2mCcbTVhoijrj9rrJcLQ5lnMerUf/pSmSyDkuMpo4/d/UkPXkOzQDzTmWQy1Rwzb+BYHc49w4gOKQD4xxvLW7Hm4mPjVMJHU3zg/kjrOV5PXvsW9dzS0FRCKQgPTrG9WZJuxX8O1rpwBwllUumFiKpdM7u78JCIpDKurbEw7vPZWI3XGiHSSZy5lemY9VF49yeOktUQM+WUJeWqNcRDNR157AsAIvETtQaI3p0DJ1MdKI90EYbkgaed1kOJmjkiYSN9Ea7zT+fkXCZeNLskI2MiWYlRzk/MqOk9h6rDVrqU0AXDa+BCsvHAVAiIbl51CRzPPJXeq99wd60t3ZFjdACPp1XuFMM6IwiG8umeQoqwyoEuqSMdcUqiShIKigNdopVUApwcIpFbhiQhmiCROhZL9Ea8yAmi9kplPUdWhQJKdqZUNHAkGfl4gdCBgWy5KuzoQxoajb1fAYznmXCdohF65JVcu4eaWaYaHRxbtfeeEoXDauBDIVA6tTBn7JtAoxCSg1szUDiRJcM2OY7YHlBxTXpBwB6VPhqTNFTzr4OThaY4ZDd38oUlUcRDggY0RRwF7ZlIV98CnO8x/2KQi6hO9UmaIopNoJWtPiaI44QzScASfbNNdErN7LDlyPs0drzOgyB5PCrZs6NcLSSMq0dEX/dh3PAHUdmmuiVTeZWDq7JE4JgIVTy3HJuBJ0aAbCfsX+8XXE9JwNTybjeOTPO3D5hFKsuqgqpxdfFFIGRHdrppJiLjg4WmI6SkO+IduRKUsUVcVBHGqM2seMEoJh+QEca4k5Bq0XBVUYlgbD7PrgagZDW1xHQaAzrGdYHHVtGoYXOhOxR5tjGF8WGvLlrf0VzbAQ13sWirHSIgipsZTpV4rUzTnu/5alD2mLGWiLZ6v4McbR0OGe/GCMoyk5AEKVKUryfA6DHPbnjtkDYq7rhgNN+PPW464GT6YUpTmaovobp2IvrGTN71Am5JNRkdGopEgUwwr8jmNJCUFpnq/L8skU7XETCdO5xI/pFpozErFx3cKJHCFJj3NP6ymoiZpMzKYwLVE+m2ngu3OkhoyR1y2OuhySBU0RPat5BUga+GjCdSRfClWmmDWq0LUiIoVhcazd0+B65y4LDxxvN1eVUS400xryFTdlYR8KAs74eFCRs5LsMqUoyVO7vJHqJkNLVEetS4jmZJuGg40djmusOaKjNdY3tdYefUdct3ocTmOcJ+UwsmMMPTHwwBAJ13DO0RA1MbI021h3xA1EdNPWm0kN5eacoymqQ+9mCQ0AS6ZVQKKkU23SBYkQNEUTGKl2ao0EFCnLAPRnMo18TDfR2KGjtIsh4e1xU+QxhrBi4siiABKm5aiiKAyoSBjOxJtfllEYAloyJBEY43h7b71dccM5MGtUIVZdJATx/rz1ON4/mBIz4w4xs5qWuOssYo9zR7vWvRfPeFpYhnFHcpUAtuJtTxgSRr6+w90bTxgM9R06nt101NabYZzjsvElWDy1wr7big40Zyw+HUoJPnPBcFwxsRT/8vpeuDn+FudZWjWZS/n+Tir2ZzKGf31jH17cVgtKCRjjuO78Snx98UTIGTEHDhG2KenHTV5nGkoJRpeEsL8+AivNCSgLi/kGiTTjn6fKMDMapVIGPt2B2Hqs1Z4OtvFgUzIpLp7/645aMA58+crx4FzE5yeU5Q2YFeNgJmFajvOdCQdPSp4DPBl/T18LE+CUHaZBb+SjCRMtLktWEYfXbAOfrjfz3v5GtMdNXDNjGF7bVYetx1rtG0Cqqib1g2GM483d9dhytMWWhc1Mw/pkiiXTnVo1hQF1wHlXskQAA/jXN/bhpW21jqz/i9tqkTAYHlgyGT4lQ5PFYojpZr8vET2TqDJFVUkQhzMSsZUFftS0xJBeCxBQZNS3J2xt+UwDD4g47QeHml1nkjEO/G1HLdZcOhp5PhkJg+F4axyjij3FynNN+sotpptoiuh26C41wCiVXE2Rqs4T85tP/UY9qH91jPGcypJNUR0dCdNVssBkwMfHWnGsJYaWqJ70zMVrth5rBQAsmzEMAPDarjpsq2l13CRo0sr7FArGgSXTK/ClBZ1aNTIlKO3njU9uyBJBTDeFQc+IKSZMhld31uFzl1ShOM+HcEYlUYdmwi9LQ9qbzPPJqCzw40SaBLFMKSoLAkI/yeL489bj+OBQSsWUY0JZKGecvqtAIgfwxFv78NA1Ym5oa8xAUE0M6RXVucZi3JYG+cVb+/HSJ7V2s9zlowL4esUoNMUSKAn5bIcwFZaRemnggdMw8owxfP/738eePXugqioeffRRjB492n7+0UcfxZYtWxAKhQAATzzxBAzDwN/93d9B0zSUl5fjRz/6kT3Y+0xQ35FwFR6LJQd8d0oWuP9cMuViAeFBbT3WioVTRGeiW408SwqS/fSGmRhVEszqAK3I9w/IGLVCKRo7uhDgokBzTEdAFTmN/LR8A+Mc7ZqBwuDAu7n1JSV5PmgmQ3PateWTJVTk+/HLtfvxwSHnqnJffaRH/QlubDzUhLhu2ddfbZtmzwb2OPtEEkK99Rdv7cfLn9Q6kq/rDkWx7t82wCdLsBjHshkV+OpVEzq999Mohe21pXnjjTeg6zqeeeYZPPDAA/jxj3/seH7nzp34zW9+g6effhpPP/00wuEwnnjiCaxYsQL/8z//g2nTpuGZZ57p9YZ3RzTh7FxNwRhHY4coN+tKsqArKCHo0AxEE2bOu6tECYJ+KcvA5/sVhAdoNyKlBBX5vtwCXAwoThpxzbCyuvnihuWpJQIYXuDP0i+SCEkz8J1YvGuPvStSk85ScC4apTx9m3NDSr31pU+yV8IMwjmMGxZ0S6yK/23dAciUJmdY9J5eG/nNmzdj3rx5AIBZs2Zhx44dnRvMGI4cOYLvfe97WLVqFZ5//vms98yfPx8bNmw4nW3PieUSptFMhpqWmKPbNSVZcKp9SIxzhP0KRhT6c94kmMtQEJmSAZdszaQgoOK68yvhzzhoPpni6mnljptaXDcRSwijHtNNHG2K4WR7/Kxub38kpViZnsRvjuqO+a7pKFLvfuSMAyG/82aiGQwn2736+bNNwrRgWqIfp7vmJfF6hr9+ctIuQT4dM9/rcE0kEkFeXufwAkmSYJomZFlGLBbD5z//eXzhC1+AZVm49dZbMWPGDEQiEYTDYQBAKBRCR0eH62dXV1f3drMAAA1RExFd3CktxvH8jlZsOBoFJbWwOMf5wwJYMiEMk3FMLmBoKfNhe132NB43ZAJMKlERbWuAklAws8KPbSfjDq15hRJcOjKA2pqjjveWh2Tsbep9mEbTtNM+NqdL3GC4djRFa2sQ6w9HQYk4xheP8GPhCIJDhw47Xs8Yx8t7O7D+cBQSBSwGXDU2gK8xPqBlcfviXOgWw7E2A4yLH7Vl5VD55BznVfiwsy7hEMGjAEYVymiJW2hPOJ0NiQAzyn2o3n8YFXmyo9zuEIDhYQUS08/59XS69IffRE9oiwubFDUsmDnOcyYEHFt27cOwsIKOPPmU+1RS9NrI5+XlIRqN2n8zxiDL4uMCgQBuvfVWO94+d+5c7N69236P3+9HNBpFfn6+62dPnTq1t5uFSMIEaYkhNVTtl2v34/2aOETVkvghbK/TUBvlaIgk7ARXaZ6K1pjhiK/LlKAoqKAlZjiqa5ZNH4bKQj8oJfjC8OF4btMxuwSTc2DpDJFoTTdi+X7F0XreG6qrq0/r2PQFhsXQGEngh5OFd17fngABcipPPrn+IN49GoPBOFKVY28fjmNYOcMPPj3j7G14H9NX52KcZuBIU0xcN8eB16vrHEv5lETx9bNG4H8/rsEHh5oBcFhMXM0nOiyxakxep7IkKrxS75EoEZOrMhKuskRgNdec8+vpdOkPv4nusBjH0aYoii0Gi3EsnQG8vqvOVZMmHQ6C2dMmIqjKGFUc6LYufvPmza6P99rIz549G2vXrsXy5cuxdetWTJo0yX7u8OHDuP/++/HnP/8ZjDFs2bIFn/nMZzB79mysW7cON9xwA9avX485c+b09utdsZKTnFLEdQuv7nAfxdbZ8i2MektSLTDToC+ZVgGTcbtO3idLKAl3Co1JlGDVxVW4/oIRMEyGiRXhLIM3GMI0KRSJ2hUBQVXGmFIZDTk0f+K6hdd31Wcdf93ieOajY3h42RSEfIO6wKtbwn7Frri5a944AEKiOLVCSjfWN84ZhWtnVuK/3z+KPXUdMBm3Y/htmokZIwqwdEYFSoI+W7cegLimqVC9JAS2omFDdGh3I59pGOOwOEc0YSJhWnZz093zx8KwmJAn53D0TqTwyRTXnleJoCqDEJyWBlGvf2FXX3013nvvPaxatQqcczz22GN46qmnUFVVhUWLFuHTn/40brrpJiiKgk9/+tOYOHEivvzlL+Phhx/Gs88+i6KiIjz++OO93nA3GiPOapqmaEJ40z1YHVlc/BjuvWoCEqblaHxSKbE9oXBAdpX9DKkyRlYEXCtPhhUEBnRoIhNVpg6da0qJ64XaHNOFHovL8ZcoQW1bHBPKw2dwSwcGJXk+GMl47T0LxtsSxeGAjOZowlFDT0Gwt77DtW5+V207Vpxf6TDwjHHEDQtxw8DwwiAkQmBYHD6ZIqILmYSi0NCueOprOOdJ4y0897aYbucBCQgkCnzukiropoV39zdl/TwoAa49rxL3LpzQJ9vTayNPKcUPfvADx2Pjx3fWgt9111246667HM+XlpbiP/7jP3r7lV2iGVaW6E9JyOdqfHJBCUHCtHLWEgcUKav+GxAnriLf72rgCwKKY7DDYCDTyKsSRTzt5hrXLTTHdAQVCS4VrACE9zLUvfh0hhX4YVgMrTEDAVXCCFWE9vwKxfGWOFKLoTYtd9kvIaLstyxPrBo5FwaecQ5mCS2bsrAPnHNohgXd4jjRFkfQJ3WpV+7Rc1Leu8U4LMZgWiIOT5Ay8AQdmgXD4nh3v/tYUYkS3D1/nN09frq9JYPmV+YmExxQJSycWo43q+tyzmhNJ1U144YqERQG3Z8rDCpZXZ7iPRQVA0An/lQRBqHzhppapViM4z/ePYTXd9WDUlFSWVnox8k2zRF/VCWC686vBAGBabEB2TNwJhhZFIDJOCIZg0WGFwZwvDUOxoCCLlRPOQd8aceyQzPQFNUR9ovVZyRhIj8owycJg54whaRCTUsc40o9WeLeEk2YqGvXUJrng1+hSQMvjH3MEMkTiVK7qsawGNpiBiRKchr5poiOYLEwz6cbBBgURr5dMxAzsuOLjHGsOK8S24+1OmRXg6qUVHbrfG36pKd0dJMhbpgYUxJyvaMGVcnV+BMQDC90D98MdCRKoEjUHgySKvH7j3cP4Y3qZAw+6ejXtsZRWRhAbasmDD8H5o8O4uuLJ4KDI5Iwh3yDVIpUaeXBhohDzMwnSxhRGEBNaxw+RcIlY0uyauoViWDmyAIUBBRYjNtJ2lR+aU5VEZbNGIamSALDCzrlDeK6BZkSNHQkUD5I8kZnC9Ni+OFLu/DHj45BSoYsPztnJB5cMgmUElAinBhFoqBUdK2Kma1i9GOuKANjzlGgva2qSTHgjTxjHPXt2eWPFuNojCTwzKajaMiYqGNYDGVhHxojOgiEB3/eiAIsmVbh+NyUbo1EO4XLVl7YOWtTpgRlOUI75WHfoO4s9CuSbeRliUDTWc4ka22rhifXzEbMsFAcVNFWf9xeisYNC0GTDYihKWcDiRKMKQ3hQEPEMUREGHo/jrdquH7WCACw5Q8YFwnaa6YPQ0Q38actNdh0pDkZtxefseVoCwDg2pmVaE+YyE+Gyhjn0C2G+o4E8pMKrB4944cv7cIzm445Vqn/b0sNOOd45NqpSSPPIUudXnw0GeZUJIrKfD+Otjj7RhSJYPHUcofO0+kusAa8kW+K6o5kq2kxGBaHZTHUtWp4/2Bz1pLIsMSNYdKwPOyrj4JSgk+Ot0GixBYfe21XHbYlJQtSSa4NB5oAAKsurgIlYmSfm6ce9iuDPpnllylSXQ6EEHQkjJxJVkrERPpA0rBohkhIpW6WkYSJYnlwH69TQZEoxpQIQ5+e0/DLMoYnK3E+O3skVpxXiTbNQJ5Pxt92nMT3X9oJQoirVrnBODYfbcHiaeVoiSYQSqsA0wwGVaKoaYljQnle1ns9soloBv740bGsMkjNYPjfLcfxYFKoj1Jid6zGDRMsaYt+t/EwTnZkO6eV+X7cccVYx2ND2pM3LOZQmNRNZnuX7QkTzV1o0zAAu09GAHTapa3HWsE4x+yqInx8tCVLMtiwODYcaML1F4xAVXEwZxy+cggse2WJQqbUvsEOLwjkTLImTIZv/e8OsSJiwCUj/Zg0wURhSEk+b3mx+Qz8ioQxJSHH+EBAKFQOKxB5Dp8ioVyR8KctNVmaN24QCKE4nyw5holwzpEwGQix0BhJoNQTMesSi4kS7K4kTZpjIgGeLkkQSw500QwLb+2pd43Hn2xPZK2GuxpI1BMG9K+qviNhJ6ESpmUbeM44OuImCvzyKWnTmIxjy9FW/NeGQ66a8EDyrsrhWhlCyeCNw7vhT7vJFQQVXD2tHL6MsAuBWG4aFodmMOgWw/vHYvjF2n2OYd/RhKdpk0nIJ2NUUbY8cEiV7RGCCcNy1bxxw2Tcrg7r0EzH8U95/yfbNG8IeA44FyP4GOcoDio5Y+oW56gsCDgq0CzObR15IWHhbiMsJpoN0znd8usBa+TjuoWO5IQV3WQw0y7y9oQJi/Nkkqr4lLU/urrGOQfGlIZcn6vI9w+pmGYgbV8pJfjSgvFYPLUcqkThV6itq5/5WzAY8PquejR2dHqTccPKKXw2lCkIKqgszF4ZhlQZFWE/2hNGj5fz6S/TDAtHWgxbMI4lDRjnwIlWT18oE85F2JZDhISDPhmfnTPS4egAQEChuPnCUfArkuNmmS7M11XS1eLAS9tqHY9lDuI5VQaskU/d7SzGHR4J58KLT/HpWSNwydhiyLT3Qk8pVIliacbwjxSFAXVAjfLrC1IhmxRBVcbd88fhd3dchEvGFqOrw00pcLI93rn6Akd0iM+DzUVpng/l+dkhlDy/jPFleT3uBZEpRVvMwMvba/GTV/bg99ta8JX/2YLfbTwMi3E7TNChmWg7hUHTgx0rLS9nJo8RJQSPLJ+ClXNGwa9QhFQJfoXipgtH4bsrpjm8eMBp5P2KhPkTS3N+39t7GhyzkU/Txg/MmHxctxDVTXDOs5aWMd1yDDmWKMENs0didhmBnFeMn725L+cc1lykbg5Lp1fgS1eOz3o+qMiocPkRDgX8CkUkIc6BT6FIrTQ3HmhGV+NxU7LEcd2CEhBXcUy3kOeTvXptFyryheJp+uoHAMrDfswdV4x39zd1+xmMc7y7vxE7HZOmONbtbQQA3HZZZ8LvRFsceX55UHVq9wbTYo4sR/psVVWS8cPrZ+Bb10xBXbuGiny/HcaNp90kObLt1NXThuHtPY1ZA9lT35FeJz8kPfmUF29YPCvmnqlhnkKVCEYWBTB33KmFbxSJ4FvXTMYf7pqLry6ckHXRKxLFiKLuxYMGK+nhKYkSyBLtlDPIAQFsWeJEstIGEEYo0wPy6KSyIIBil4liX71yYrc/ZJkSTB+ejx0n2mFkODm6xbBubyPiuml7qqbFh3TYJhV/zzTBhIj691TtOyByJ+PK8hx5ukSaFoVuMkfynIMn3+/+3Rbndp08IUMwJq8Zwotn3BmmAUS1TXfKbqnwjSIR+GQKmQJzqgpdY/eKRHDFhFJcMrYUeYHsRY9ExI1jKHs7SkbIxidLKA6qsLpJBK68cCQAccGnqg4ALwHbHSMKA1nNd3l+GcvPq4Tq4rxQIgz8zJEFmDO6KGfNNSVAS0x3rHJbYwYiiaEXQuO8c5h2Oinj3t3vXTeZo9Is03GJ6hYsi2HmiMKsWRaqTHHN9Aq7Tr4vbMuAC9ekvHjTxYj0xECkwjfXnleJNk1U4MgSxZ8/rnF8JiXAZeNLcP/iSWKAdQYEBCOKAp7mB4CQT0JbPBmykQkCqoTLJpTYYYBMFImgvj2BorQpUnk+CYQQtGs6mqIJjCoKeto2ORADuWMOraa75o0D48Dr1SdBCAFjHLNGFuLiMUVQFQmqTLM8ynQY5ygKqlmhzBOtcUwszxsyK1U3Ay8RckoVc+lePCAGFqUwGcPvNhzGxoOpRjbhaUsUIITiqkll+MpVE+3Xn275JDDAjLxmWMk5idx1dmvUxetgEPPTMkeepWqMAdGl9uHhlowTC4R97po0gBCUSu9KG8oEFAkdmlhdyRKFKku4e/44vLOv0XU+KeMcIZ9kN0RxzhFNWPj39Qfw4rZau0V81UUiieXVz2czsigg5uYmiwwkSnDXvLH4zAXD0RzVYTDhTWqGZRtuVaaYObIA22vaHMZcoQRzx5XAr4hzwjm3jXrCYEL0LDw0ck4sOW6RElHh3pty6HRJCt1idgMUADz13iFsPOjsaVAlgmnlPty/9Dz4FclRhtwXnvyA+vXYXjzjWR5JegYcSNalmhZ0g0E3GXRLhHcyo2yiztilK5YJXe+4nr06KAn5hlwlTVcQQhyx+YAiIc8n45oZw7LkChSJYHZlAH5FQjztx/Cvb+7DS9vE7MuYbiFhMjy76Rh++NKus7YfA4mUzk1emiqqxTj8ihA0G10cQr5PRky30BzV7cTfwsnlmDmyABKB/b/ZVUW45rxhADpLBdOp79DsWP1gJ6XLJNFT897TSffk0/+tGRbW72vMsjW6xbGzTmhrEeLscFX6QO5jwBj5hGnZ8UG3UE16iZJhMRguS1OLcRgmc2S02zQzZ52xRAiaos7GhHy/MmS8mlMhmFZW6lMoKCG484qxWDSl3KGiZ1rcXhInTEvI4eoWXttZ51jWAmLU4DObjrmu0DyEoR9dHLSHgqcXIViM44VPTuAXa/fjtxsP4xdr9+ON6rrOXgRCRHw+qX2TMJj9/sySTMaAOpcWfI9sDMsZj0+kOTL1ES3nrFZCiGuTlHK69ZMYQEY+VbfLeHZFDdC5RDIs1mXdMOdwGPquumItzh3DuAOKhMqCwS9Z0BsUiUJNC6sEVFF+l0r8peAAtp7U8MePjokSWIt3WY0jEYI6b/B0TiglGFMSQtAnOUJj//3BEby7r9GeHmUyju01bfjdB0ewvaYtufIVBv3jY6342ycn7Zus2++nJao7HCkPd9KPEUsr8bYYx8vba6HnKEjQLY6XPzmRpUpxur09QC+NPGMM3/ve93DzzTdjzZo1OHLkiOP5//qv/8LKlSuxcuVK/OIXvwAgloHz5s3DmjVrsGbNmlOaCsU5R1tcGPlcBlw3GUzmNPAJ00JjRyIrEQKk6l87u2IzKxN8srPxySdLGFkUHDIJqN6QnigNKDRNmTI7FLZ+bwOONEXRETdRHFRzDxfhfNCMTjxTUEowtiSEQDJ/pBkW3t7bkHXcTcbRGNFdp0ptPtpir5TdnB7O4Rit6eGOCDeaONYcczSU/W7jYVvgMBfv7G/CUxsO2X8Tgj7JR/Uqc/jGG29A13U888wz2Lp1K3784x/jV7/6FQDg2LFjeOGFF/Dcc8+BUorVq1dj8eLFCAQCmD59Ov7t3/7tlL+vXTNtzzuXkY9oBuojCYT9MmRK8ddPavHR4RZQKioNppWpWFnRqXzIuQgdKBLBmrmjEfYreLO6c9jF1dPEMG5AGPhRQ7xUsif45M75r5QSRHUzpzKlyYAf/W0PAGDJtAosmlqOt3bXO0pg/bJoEfeqbLqHUoJRxUEcbYqhti0uxvx1IVaW9X5C0BE3UJ7ny0q+pujQTEQTpnc+cmBaDD/6W7UoHiCieOCqyWW46cJROQXJ0tFNhter63HfQjG8262qrzf06mxt3rwZ8+bNAwDMmjULO3bssJ8bNmwYfvOb30BKTp8xTRM+nw87d+5EXV0d1qxZA7/fj29/+9sYN25cj76vPenFp2K56ViM46n3DuP1XXW2QS/NU9GU8liSr9/VkMBfP6nFdecPt9/LOVAcUhD2K7hr3lh8bm6VPfMyzyfCDapEMaoo4FV49ABCCII+2dYUGlHkz+mhA7Av+jeq67FwShkWTy3HG9X1dnXNivOH45Frp56NTR8UcAAjiwNIZOSdegLjHMPSQpGMw1WWorZN8+SIc/B/X9qFl7bVOrpb1+5tEM5ODjXcTCTS2e2q9JHN6ZWRj0QiyMvrPNGSJME0TciyDEVRUFxcDM45fvrTn2LatGkYO3YsGhsbcffdd+Oaa67Bpk2b8OCDD+JPf/pTt99lWMzWNHFz4p967zDe2l3vMOgnXYaImAzYdKQFS6ZXwCeLuuGSkOqo/ggoEgKFgeR3ia60UcVBz8CfAkFFQkQzwcGRH1CxaEoZ/razrsv3JEyGN6sb8Ls7LsKtl44BAJSGVQRVGRYHvDqm7kmVCBNCMKEiD4umVmSNvVQkgqKgguao4SyhTDb9hVRnpY7byjWuW2iLG151WQbRhIlnXfTldZPhg0PNWSXcuWBp3a59kXQFemnk8/LyEI1GOzeMMchyWktvIoHvfOc7CIVC+Pu//3sAwIwZM2zv/sILL0R9fb3rkhAAqqur7X+3aRaa42K9n0og2d9jMry+62SXqpHpmBbHgSMnMKpQRUilONGS1KCQSVaFjUwBqUjF/sb+Y+A1TXMcm/5KRLcQN8R5umwY8Nou5JRuTkHAsX3PIZTnyQj7JCSaxfnwSQT5/v7XcNbfzoXFODoSnT+ElRNltLUF8NHxmD09Kt9HUN+h2xUelIj/zazw4dIK4Oixo/b71WRHuBsnawhGFvSPIS/95TzUtOkgOTz11I22O19eocDlVQGcOHYYAFDkl7JULntDr4z87NmzsXbtWixfvhxbt27FpEmT7Oc45/jKV76CSy65BHfffbf9+C9+8QsUFhbii1/8Inbv3o3KysqcScypUzuX6IcboyhMJk7FcInOw3SiNQ5ZqndtjHKDA6jRFCydOMbxuCJRx9JIpiJEEw4ofbZk6guqq6sdx6a/YlrMHrk4Qjchvd0Aq5s6aw6CmZPHIqBKCKiyrXtOQFCR7+t3Ce/+di5Mi6E13pnoi+sm/u8YhprmGA41RvH6rpP44JAYAZj6BTEOXDS6CEumD0NhUEV5WmmwKtMum/1Gl4f6RTNgfzkPVQkT/KUT6C4kQ4mwN4xzlOb50NChQZYoLIth0bRheGjpZFsmpLLQf0r2Z/Pmza6P9+osXX311XjvvfewatUqcM7x2GOP4amnnkJVVRUYY/jwww+h6zreeecdAMA3v/lN3H333XjwwQexbt06SJKEH/3oR91+j8U4tLTKmExbXhRST1mDfMOBJnxubpWjecdkzD6YMhV6NIospq4PIXn4PkOWKPyyBM20EFRlrDh/GF7efrJLXSHDYnjqvUO4Z8F4JAzLNvIcYmrRUNLp7wtSP4uRxUFQCjz6cour+fngcAu21rSBcY75E8uwZu7o5Ezjrj+/sUNHVcm5N/L9hZBPxorzK+2GPjc4RDnj166agLKwDz5Fgk8hiCUYOppPYtaUcbaBJ8mbQV/Qq7NEKcUPfvADx2Pjx3dK8H7yySeu73vyySdP6XsyhX0yS7sCioSrppRj7Z4GR7JDIp3tydnbTtASM1BZ0Gk0OBeDu32KhJGFAbvLrKc63R7ZhHyyfYP+xtWTYFocr+yoA6VJAaeMQ8sBvLqrHrvrIvjnm86HYTL7PGiG5Rn5bsi8UtNjwDHd6tK/TBmld/Y1gBLg1kvHdOs8tWsGdG8Au43FOL565QRwBry0vTZrhJ/9Og68tbcen7t4NAAg5FNQGKA43O6MJvTlce3XZyhdOD+Xwf383CosmFgKVSLwKxSqRDB/UmnO8iPGOIqC2UmjVIgmvY2Ycd7jhImHE1WmtnibTCkeWjYFT99xMf7ppvPx/avKoeQoRz3SFMMv1+5Hm2bYYTjNYN55OEXSTUwPo5nQLaEtrxld3xQA4Rhljqkbyugmg0wp7l88Cc/cPTdLXTKd7TVt+N+Pj4NQZ3LVYeT7MEzcr9db6boxuX7klBDcetlo3HTRSLTEDBQFFdvrW7fXKZBFCXDFxJIsrzCoyBhe4F4myTlyyrN6dE3YLyMREedQogTFeSr8KkXNseS0mxzGZ/2+Rqy+uAoE4gbhVykSpuJ5812Q9fNI+3t4gR+UuFenZZKSHPYrUs7CiBQtMR0V+X6vfwRweO75QQWLplTkrI03LI73DzXhhtkjHI+ne+9DwpNnjDvU3NyuT54mceBPSg6kLk7GXeI1HHajR4p8v5ihyXNcp6cyCNzDiSJRxxzYkE8CJQQFftqld0kJQVNyApLJGCKaidq2uDdg+hRIv2x9ioTFUyvQE1vMOGwJ6O5uCowBrTG96xcNEdJnW5gWw62XjsElY4pzvp4SgmiaEysTApKmbDMkjLxmWkhXdXaztbnsbyRhYsOB5ixHkQHYcKDZbt8WFQV+EAi5W7c4pGfiT488n2xfvIQQhHwyfDLFwillOd/DOUdBUHYoH8Z1C61x3RMr6yHpDjjnHLdfPgZXT6uwSyMpkCWWpUoECyaV2iumnoTIck1iG2qkV/2ZFk9KP4/LqT3DOEd5uLMMNX2R2pdJV6Afh2t6kvTMnt0iaIoaOTvMKCFoiRoYVxrOauhgnINmXPqeJ396yBJFQJXs/EpAlSBR4J4F47GrtgPHWpwj5lSJYN7E0qS2OZCaycI4h2mJYd+GxVAQUPpdWeW5pLtDIVGCO64Yi1suqUJzVEdBQMFv3tqFTcfjYsgI57h0fAk+d8lo+z09ufJT8x2G+rlI9+SN5DLVr0hYMKkM6/Y2ZIVtSvN8kAjFidY4ikOqI4eYqz+ht/RbI59dfdEzL5tz3qWyJOMcE8vDyHcZ53cqqwWPnhP2ydAMyz4neaoEAoLvXzcNT79/BO8dEFNyOOeYN7EUt1xcBUAIZ6WLOusmgyxJ0C2G1pjouuyt5vdgo6dHIaU3DwDXTy3A15eeh4ZIAibjUCTplOPrnItxdnlDWM/GtJyy5umhyM9dXIWdJ9pRmyHudrJNw12/2wSfIkq1r6gKYupEkbzt62lz/fbMZC4Ve2qAORcX8hUTSvDe/iaHEp9CCRZPKUdxSHXV5nC/afRi4z0cUCrCNClNG4kSyLIYzHD7ZWOw6qJRaI0ZKAw6k6uZN2rhLYnnDSaafwo9Qw8A2Z40cf5bM8TwkOKQ6hzwokqYNCwflsVQ3+E0RD299js0Y2gb+UxVz7QDFzct1yqk1CtSecf3jsbwi7f24/7Fk3JOo+st/fbM9OQCc/PuU5OfbrpwFADYI+gYFzH5N3c3QJUpvr54IgKKc/ddbxpeVL5PCKkSYolONdGAQiFLFKYlGp2GFTi9F4MxMEMkoGRKIFGSNbjd9Ay9Tebep/62GMe/rzuIV3aetIXfFk4px22XjQHQec1LEsXwQiGlfbItDlG30LNrf6gPX8+siedpRr+li9Cx8zM4Xv6kFvcsGAefHOjT7eu3Rr632BctJVh9cRUYBzYeEB69xTgscLyyUyhWPrR0iut7PfoeQgjy/LJjLkDYL6MtZoBxDs2w0BozkB+UYTHAsjgkidn19LJEEVAoDJNDkTtNmskY2jUDhcH+oaVyrsh05FOG5Vdv78dru4RQWSouvHZPAwBg0UjqTNACKAoqCCgUJ05JO35o/3DSk64Wd44mLQwqPc7rUULQHjf7PL/Rb4180CcBHafzCQSqRLDxQHPW8ISEyfDXT07i3qsmdKu/4Rn+viOoyrbXx7m4EQdVCf+27iDW7Wuwtejnji3G9bNGQEqLp5kWQ4fFoMo6SjPGL+oWQ4dmIOwfusqIJDl4OnW5EoiKpFd21GV5mrrJsHZ3A64YVuY6+tKnSBhTEkRct9CRMHvQTDW0V1HpVWBWxsHyKxLmji3B+4eautWTZ5xjRFHfD8jptyWUPlnqdRlRQJEwIplcypVIooSgMeKs8Y3qBg43RhHzyvTOGHZFU/K0/NfGI3hnvxhurJks2SjSjOe31KCxI5E1ci6asNAeN8AzDE/csIb8eLp0g02T84lzXv8UaE8wxA0LNS0xxHXLGcYnBOX5fkyuCKMs7Ouyeqevq0EGGkZaeMatKvAzF4zA3LElUFLlq0n1z3RUieDa8ypRFOz7+dH91pMHRFNGZjKoK3yyhLI8vz1TtCTky1mKKVTgxBLfZAz/+uY+MdElGbe8YfYIPLR0MtQ+znQPdVSZIqAQ29N8bWe2p2lYHBsPNmPzESGqdeWkMnzukioYFkNdRwKUhmAxjsKACpJmXzo0E4pEh2wHJk2uhADh3HR1/VsWx/rDEfzrxg/ta375ecPwreVTbJEsQITJhhX4UZqnojGiozGScKxuCRHlgEMVzjksK7eRT+WTbpwzEtfNrITFOcrDfjy76RjW7mlIisGJ6pr7Fk04IzfMfm3ki0MqYrppNy9lkuoRCygSwn4FYb8MgzHoyYx1QJVwzYwKvLKzzqEM55Mplp83zA7V/Oub+7LU4/734+MAgEeunXaG9m7oElIoFEqT0+nhOh4QgB1me3tPA3af7MDJdg1Ssqb78gml+PqiiRhe1Jmk4uDoGMLx+XSpiIRpoSmawOKpZXhzd4Pj2lZlimH5Pmw5EYfBYB//v+04CVUWOkOZpIx9Rb4PCZPZq6aQr+8mGA1EMo16Kr+UqmRK18IKBxS7m/gLl4/FZy4Ygda4gckVYbTUHUNAkc9IAUG/NvIAMLIoiLaYgfp2DTHDtL2IgCrBJ0uQJQIpbS0pZawrv3LlBADAXz85CTmp47xsegXuWyQej+kmXnSRB9UMhv+35Ti+sXiSN9OyjyGEoDCkoDikohuZeQBiOZxqmkrNLV27pwHr9jTg07OG48FrOjW4dUsMUu4PWudnG0oITMbwT6/txV+2nhCePePwydRxfZeHVdS2aTAyjn3CZPjL1hO4d2HuXBUhBH5F8nSEkqSXT5qM4Ym3D+D1XXWdlUyTy/GpWWLkaH4yVGkxjt9tPIy1e+ohUQqLc8yrCuInZ8ifHBC/hIKgAr9Ks7RLDIshkbxSY7qJxoiO0jwVJNlYA4hl630LJ2LhSIKCsuEoCfkQUCWoySlVjRE9591ToiJuX57f98mQoU7IJ6MwqGLJ9Aq8vquuS635XDAAL39SC0IIvrW80/uMJiz45FNv7BnoUELwT6/txQtbTziOZ2Y4rK49kVOXRqIEDR0JjPa04ntEuif/i7f2483qemcl015RyfSFy8far/vdxsNYu7dBrFQtsSJ650gU//z6Pvx/nzmvz7dxwJxJ4pLBT3kuqXh6apD38hnD8KUF4x0/cr9MMbIoaP+d8vhL83IPHrEYR0X+0I03nkkUSpHvV3DPfDHM/bVddaAAtFM09rrF8dIntbj9sjFIWAxlydmwkYQ55OaQxg0Tf8kw8G50VeVhMY6yZPWSW+WNh5NUDiSmm3jpk9osR1Q3GdbuqceVk8tQWSBCi27qlLrF8actNfjO8ql9HjkYMEbezSmjxD2e/tcdJ8E4x30LJ7p+lpSWWAqqMq5LTnRJNzB+heIzF4zwQjVnCEoJJImgKKTiSwvG4bZLR+N4axx/2Xoc7+1vzjl0wQ3LYvjsv22AIokW8U+dPxzfWDIRQbX3FVoDkaaI3uPVi5Ss8EgP2fhkik/PGm6Hajwb3z2ppGtTRM8KFafQLY6/f3EnOAcuGVMMiRA77JiORAjq2jWMK8vr023s9S+AMYbvfe97uPnmm7FmzRocOXLE8fyzzz6LG264ATfddBPWrl0LAGhubsYdd9yBW265Bffffz/i8bjbR7vi1iAQ1y28mGGcARFbfGVnnUOPPp3MgpmvL5qIFedXwidTBFUJPlkY+IeWTvYu9DOIKlOoMkVIlRFQJYwqDuK2S8dgwaRSKFQMNu4JFhfeaUy3kDAZXtx2Av/82r4hp1g5vDDQ42lmEiWYOyoInyzkoH0yxYqZlfjmks55zZ4n3z2pmHxJnmp79W7opgjhfHA4twNjcY6KMxAa7rWb+sYbb0DXdTzzzDPYunUrfvzjH+NXv/oVAKChoQFPP/00/vSnPyGRSOCWW27B5ZdfjieeeAIrVqzADTfcgCeffBLPPPMMbr/99h59n5uDUt/RRR1wsk54pBp0Pk6Jo0QMEIMpHrh6Mh5cMhn1HQmUh30I+joHSXucGVSJQjMshPwyDMadnYG2gTn1bjTNZHhh2wl8deF4BFV5yIyoC/lkfOaCEfjzx8e7DHv5ZIql0yuwfLSEv1shVlAAx9RhYcdvY4ilNHpF6qYaVGWsOK/SNWSTjmFxUCArGe6TCG6+cNQZiRz0+urfvHkz5s2bBwCYNWsWduzYYT+3fft2XHDBBVBVFeFwGFVVVdi9e7fjPfPnz8eGDRt6/H2EkCxvvjzcdR18ZsKUEJKzDpUSgqBPxpjSkG3gxeM93kSPU8QnU/smWuBXoEgS/ufDY1i3t9GRvOoNIoGo51zNDVYeXjYZn5o13LEqHVMShCoR22NfOr0CX75yAizG8R/vHsT9f9yKB57djmX/+i5++spumIyBwH317CGwGEfCtBDTTUR1E5GEgdsuG415E0TTU1eOhSITLJhY5lhFLZkYxndXnJnyml7fNiKRCPLyOmNHkiTBNE3IsoxIJIJwOGw/FwqFEIlEHI+HQiF0dLjrFlRXV7s+rhkMmb/7q8YE8dahqEO6QJUI5o0OovHEUaFXwzksI4HjRw7mDDQq1F2oP6CQfrNs1TQt57EZSKTvR0fCsjsGY7qFtbvrskr7eoNpMbTXHcOOZooCX99X2vTXc6GZDJ8ZJ+GaUSPQolkI+Qg4I9BMhjbNQoFfgl+mOHLoEP64vQkf1CSgM27Xyv/54+NobW3FnXNKUO/v/2WSZ+s8pOyIycS/U75lQ9R0rEDnD6eYWVyMmnYD/29ne5a9AsTUu09PkHD9xEq0xi2MzFcQli3s27vnjGx7r418Xl4eotGo/TdjDLIsuz4XjUYRDoftx/1+P6LRKPLz810/e+rUqa6Pa4aVpUT4owkT8Nhfd+OFbSfs2tTrzq/E1xdNdCw99+3fj4kTJuTcH39SFTEdQki/klCtrq7OeWwGEun7oRkW2pMSxEeaYpClkzBYtvetUACE9Mi798kUnzp/OM6bNhmAWEr39Xnsr+dCN5l9PAHRkdkay07zxXUL779Uk3VD1S2OdYdj+L8rL7arQfozZ/I8MMahWwwJk+WMGIRa4rZap8U4XnhrH9bvawYlBIwja7auKhFcPa0CY8aOQ0iVQQlBRYEPB/ftPe392Lx5s+vjvQ7XzJ49G+vXrwcAbN26FZMmdSZsZs6cic2bNyORSKCjowMHDhzApEmTMHv2bKxbtw4AsH79esyZM+eUvtPNG5Mlim9dMwV//doVeOr2i/DXr12BB66enBV37wpCiOsQby9Uc+bxK5K9UioLqzkV+zhyi8VRAijJcIQqUyybUYFvLOmsrNIMq0ej7AYDmePmCCGuI+iaoomcK1SJEjRFhu7s1oQpHI/WuIGYbuU08Jxzhxzzb945hHf2CSGyhJkUPU8aep9MoUgEV04ux13zxsFiHNGEmXzuzK6Yeu3eXH311XjvvfewatUqcM7x2GOP4amnnkJVVRUWLVqENWvW4JZbbgHnHN/4xjfg8/nw5S9/GQ8//DCeffZZFBUV4fHHHz+1jc1hdWVKEFRlVBX3bndyfW5/CdMMdgKKhGiyS/VT5w/HC9uctd6qRDB3XAkA4P2DzkEwqkxx5aQy3LNgHJqiOkpCqhgxmOa/MC5+dEOhS5MQAoVSewQdII6vbjkrjUpCvpw3VItxVBYMrQZAzjk0gyFhWt0OME+R/rq4buH1Xdk6TAyATIAHl0zCsIIARhQFbGfV4tyhtHqm6LWRp5TiBz/4geOx8ePH2/++6aabcNNNNzmeLy0txX/8x3/09itBCEkug5xnIVUxY2bIfKZ3wXZFrlJqz8ifHQKKhJguBrenPPAXtnW25S+cUo7rZw8H58IjWre3EZSKMWsLJpXic3Or4JMoRhYFENct1LTEIRFRg59Ct4aGkQdEYs9Ic8QliUKViOPmGFAlXF4VwsaauOOG6pcpPjVr+JCRbWaMQzMtJAzWozouxrgYaMM4dJPZirUnWuNCO8glzy9RCp8ioSRPzYpG5Kqt70v6T8C5h0iUgLnEZRWZwExe2G5dsPNGB/H341hWGEei7qEaILeH79G3UErgU0Q5pUwpHlw2GXfNG4sjzTHbMwcH2jUTN188CgumlAKcYFiB3zbchsXxn+sP4tWdSd0QzvHpZFOUTLMlMQYzsou1CaoyTM2ZJFw5oxCFhQX4247OqVGfmjUc31wyadBf+ynPvTmaQH1HAmVhn6teT8qoWxaHmUy+ptBNZhcNhANKl5V+RSEVQdXpZKiSyAOe6VDigDPyMiVwkw2X0rx5ty7Y9Yej+Nc39+GBqyc73ucWrwSEFz/UR8qdTUKqnPSmxAVfFFJBCbHDDhbn+P37R/Bq2hi7KyeX4fNzR0OiBL959xDeqE4ul5PXx4vbTgAAHlw2GYwLz2so1MwrknOACCBupHk+CR2aaT8uSwTfXj4F31wyCQ1phm6wX/sJ00KHZuAfXtmLP289bl9P188agQeWToJMKRKmBd1kWfNbu+Ki0UX46EiLozhAlQgun1CKinx/VklqQD07K8sBd8XLEs1Zv+tTCOKGexesbnG8uK0WMb0zNqlI2RU1KYaauNW5RqIE/owW1/TGkCfXHcTryTF2miGGi6zb24jfv38EuslcRc5STVGpc55ZmTVYIYQ4JG5TyBJFQUCBX6bwyxR5Kk1O55IxuiRke7LyWYgTnwssxtGuGYgmLPzDK3vxl63HkTCZ3Sn9l63H8dNXdqMtriOmW1kGPq5bONYcc/ReWIzjdxsO4yv/vQVbjrbCYhwEwrgryVzSnVeMde3PCaryWelHGHCePJDy5rPvsIQQtMe7V5WsKhbeiirnPriDfbnaHwmpMhIms0MKskQQVGQ0RRN4ZcdJxwQeQCyX397dgGXThombco4VXkOHjtEl8il5ZQMdVXIPUVFK7Ga/XDkndRDq/WiGhbhugUPk6v6cNPCO15gML26rxe2XjXV42RbjeGLtfvz1k5N2SeTy84bhrnnj8N/vH8G6fcnmveQaSZUIZo4swI1zRqI8329LDKeTUkk9GzfUAXk2uzLAlQWBLlUlS5PJj4Cae0WQq6TS48xCKUEoIy4aTIYYclWCMM6hKjT3BCTGURZOTgAbIp48kOom7h2DSdSNczFIJpY08ADQ0I0cSmMk4XjsF2/twwvbTkC3GDSTQbfECvFf3tiLtXsaspUnLY7tNe0oyfMhkCPZH/KJx89G+HBAns2uQjZBn4wbZo/IWvqrEsF15w9HQUCFX8n9fsDz4s8lQuvfee7Kwz7XzkFAiJMVhVQsnV6RtST2yRQrzq+EQiVRCaFbiOsmDIvBtNigrp0nhMDXi2oiiZBBE6o0LYa2uJG16i/rRg4lNc5QNy00tmt4aXttVlkl48Ab1fU5V4eUAi0xd1VQSkRPByVnZ9U0II08kDthCgAPLZ2Mz1wwwqHfsXBsCN9ZPhm+bgy8+OwBe1gGBWG/4hCGi+pWzhuvRAliuoW7F4zDwsllyWHJBKokNFrumT9elMglPbCYYSGmW4jqFto1MVrSrZN6MODvhZfo66n0Zz9HN1lyBZj9nE+WsPy8Ya5OwTUzhkEiQEfcQFxnONYa73HdfDqMiRnViktTZsgngxCCgCqdFX2gARmTB8Qd0LC4qzcmSxTfWT4V9y+aaKtKHjt8EIrUvWcj0cHjyQxUJCrkJDoSoj2/LCxCbG5ek0QJCgMK/n3dQby5ux5Scpj1lZNK8dWrJmSdy8zLxWLc9uoIsaBKFKpEB0V1iSwJKedTKR/1D4LB9VryRu5GwrAQNyx8+coJ4FzMtU313iybXoE1l45GPE3rgfTCwKsyxYKJpcj3K1nNTgQEIZ+UdEbOzrEesEY+1a6tm7nPQtAnY8wpapYMxqTTQCSgSkndEMvuhH1x2wlH1ZRPplgyrQK/3XAkWT7JkSocXL+vESGfjPsWOQfHdBWh4Ry2x69KVMS1B3hDXEiVoZs9kyhQ5YF/c+vKwGu6hbgpnpMowX2LJuKueePQGEkgP+ldZ14ewwoDSJuP3i2KRLBgYik+P3e0a0VNKhyZmXs6kwxoi6Z2EZvvDV01RnmcffL9sr3c/caSibjufKeE7pJpFVh18Si8vutkVqVEwmT4246TWVLDHBwx3cThpqijnNbxmqSxjyTMAR/GkWhuee1MciUJBwq5DHxMN7GvrgPNseybXUCVUJ7nA1wMPCBszMiingm1KZTgn246H7deNgZ5PsX1hhn2ywj55LN6Mx2wnjyQnBwvU8TduqN6wWBYqg4mCCHIDyhoiel2J+xXF45HQ4eOsrAKwgl2nGgTPxiXzCwlBCfb4qgs8MNiHAbj+JfX9+KVnSchUwrGxajAh5ZNhupy7hkX8sc+mQ9oSYQ8nwzTMrqcXBRQBvaoRMNiWQbeZAyPvyoanmgyjLd8xjB8JS2Mp5tWlwNW/vO9QzjZrnX7/akQTWFQFcfSpTw7oEgoDCpn/TgPaCMPiLijwvhpe1w+WRrwS9XBiEQJCgJKUi6XJxt3xGUb1UyMLgnlTIxZjCPkE1OnLMbxzWe34UhTDABgWMIgvLDtBBjneGDJZKgSdW0iSknNBs9SoqyvSd0s2+KGaymqEPgbuDcxxjgiWvaq7PFXOxueUvxtx0kAsMN4iS6GF8QNC29W1zs0f1JQImwPJUkNpYml+Nzc0bYSaiYEQobjbMXh0xnwRh4QcrWM85xlUd0hUzok2t0HKopEURh0GinD5GAQy+3lM4bhbzucIRufTLFoarnd1PLv6w7YBj6dhMnw0vZa3L1gHIKqDN1iCCoSSMYN32RihuxANfQSJcj3y4gkTEcCW5Eowsl49EAlqptZoZZcDU+pMN5d88bBJ9MuK2daonpO0TGfLOGfbz4fRlL4LqhKCCiya3MTAVCe7ztnom+DxrL5ZalXqpFu7fQe/Q8l2ZKfOsfpiqNfuWoCrpkxzB6npkrCwN95xVgAoh197e6GnJ8tGmBEvNbiHBHddG2cShn6gYosURQGVREXVmUE1eQxHcAr2FxjIrtqeCIAGiMJEIIuG8aKQipYDkefcY6RRUGMKQ0h368gz+du4CkRcfhU7f25YFB48kCyXVuVoBksS3I4FzKl3TZGefQfFImiMKCgXTPBWOfyPL1SoqY5hoKg4mhLb44lPbIcl0WqEzoFBxAzLFiagTbNFIPdk9UQJuPQ+igHdK5IhQzUQaBRkyue3lXDk2YyPL+5Bl9bNBFBnwTNsJB+T6ckqV3FKeZNLME7+xodIZtUPX0wWSnDuXv1UkoXqNhFYvhsMmiMPAC7wUAzuhejUiQ6oJNpQxVZoigKKogbJrSMeKpfpigIKmiO6SiGahv64qDaZenkkmkVCKZdCyZj+MWb+/Hi9lrISYXCz1wwAg8um5xUKMw9Ds7j7GFYLGe4JajKWDGzEi9tr80K2QDA67vqICedg7yU3C8HkNSmeWLtfvx1x0lIRPRnpLpTOYBrZgzDfYsmIOxXIFGCDpcqLL8swa9ICKgS8s+xNv+gMvIp/MkJ6GIpJ4YBECKW5bJE+rz00uPsImbvKlAkyx7PZjGOX7y1D6/sqLMHiiyeJkI2AYViyfRheG3nyawk2piSIO65chyiCTGZKm5aePzVPXh7TwN0iyPlo/1563EAwLeXizmcbsk4j7NLd47c/YsnImFYeOmTk1nPpcfm7c7TpEl44q19+NuOk44mMp9McfnEUvzdkkkoDvkcFTJBVUJbXLxWIgR+VYJCKRSZdDuw6GzQKyOvaRoefPBBNDU1IRQK4Sc/+QmKi4sdr/nJT36CLVu2wDRN3HzzzbjpppvQ2tqKpUuX2vNgFy9ejNtuu+3098IFklSZTCVUgwp1SNd6DGxE/bcEnywhYVr48V+r8epOp578m9WiA/a+hRNwz4JxIABe3VUHChF7XzylHF9ZKMrpDMbxD6/u6fyMDDSD4X8/Po6vL56IoCrDSib6ve7oc0d3Q939iowbLxyFN3c3uJZZp8TIRhUH7cfiuoW/Zhh4QNwU3t3XiP/7qelZJZB5Phkx3QIlwsEkIJAkgtI8X79wJntl9f7whz9g0qRJuO+++/Dyyy/jiSeewCOPPGI///777+Po0aN45plnoOs6rr32WixduhS7du3CihUr8N3vfrfPdsBjaCIRgpSuoMU4Xv7EvSHqtV11uGf+OEgSwZevGo/bLx/jmAWb4sl1B/Gay4xOx3dSgvqOBMYkSzh1k521wQ8ep45ECUYVB3L2B6SLkaVojCRyjuSTKMHR5hgCiuSYJKXKFGNLQ2iPGzAYR1CR+lVCu1dGfvPmzbjrrrsAAPPnz8cTTzzheP6CCy7A1KlT7b8ty4Isy9ixYwd27tyJz3/+8yguLsYjjzyC8vLy09h8j6GKLBGkCl3qu5KOpQStMR3FYfFjDqgSRqrODsa4buX04NOxGEd5uNMoiAS/Z+T7M0VBHz7tMhw+lTxNv0lLlGBEoT+nrLVmWLj9qY8ceZrvrZhm6/P31xxft0b+ueeew29/+1vHYyUlJQiHwwCAUCiEjo4Ox/M+nw8+nw+GYeBb3/oWbr75ZoRCIYwbNw4zZszAZZddhhdeeAGPPvoofvazn2V9Z3V19enskyuapp2Rzz2bDIZ9APpuP6K6GBcYN1hOrXjLYog0nUC0CUh39DWToU2zUOCX0KZZcG9q70SVCK4aG0TN4QMAgISWwO49e5A3gD35gX49xQ2GRELD3r17u3zd9eMo2tuCWHsoag/9mD86iOvHSag9cggggEQ6JzRdOUa8Nj3vkgrQ6Caz8zT/u6UGra0tuGNOCVJ5W/HfpOBdZoFm8nsoIckKHiGFQAg5o+eiWyO/cuVKrFy50vHYvffei2g0CgCIRqPIz8/Pel9bWxu+9rWv4eKLL8Y999wDAJg7dy4CAeFFXX311a4GHoBjFdBXVFdXn5HPPZsMhn0A+m4/NMOyvbMbjojkaHrFjU+mWDGzEtOniByQbliIGRaeXHcQr+48KQSpOMeiKeXgWVNRO1ElgutnjcDDy6fYg+D37t2DSZMmI3yWdUj6koF+PVmM46NtO+0cX1f8aIpokGpwGdqdStxbyUHdD44YDf9b+8WAc0JgMlFNlVnJk7A41h6K4ZsrLnAdAt4TKBGDck4c2X/a52Lz5s2uj/dqy2bPno1169Zh5syZWL9+PebMmeN4XtM03H777fjCF76AT33qU/bjjzzyCJYsWYLly5dj48aNmD59em++3sMDgFgep8roHlwmBrT/78edg5lXzKzEvYsm2K9XFQk/f2sfXv4kNQRC/Gpf3VWHUcVBnGzTspb0CyaV4YGlk1AW8kFy0QbvB3m1IYtECQJK1yeAcw4zTU66OKQiYTLE9YRt1N2iM1+cNw6fv2Q0WuM6GAPuf2are/I2baRob2CcoyNhnNGS3F5t2erVq/Hwww9j9erVUBQFjz/+OADgpz/9KZYtW4YtW7bg2LFjeO655/Dcc88BAB577DE88MAD+M53voM//OEPCAQCePTRR/tuTzyGJEFVtOrLlOLby6fi64vFDIHSkAqSFKVKEdNNvLDNfcrPsaYYVpxfiVd31oFSApZ2k1AphZRDVKo/VE8MRaIJE3XtGiwGhFTJngBlMgbT6jTsueLrXSERAlkmyFMlDMv3I6qbuZO3GY10pwohYh5CxxlcDfbKyAcCAddQy0MPPQQAmDlzJm6//XbX9z799NO9+UoPD1eENyfZXlZQle3qF3COuGHZA8BrWmI5m2cYgE9fMBxfXTgBjREdpXmqvQTPJcHrjYk8u1iMI66b+P/+uhv/b0uNKH01GT41y8C9CyeAcUA3WE6DbHEGxoRhNpPhl1T8nIKAUvFfQoHMJtaFU8qxdnd91kpvxczKXodq/IpolDrTulle4bjHgEeVKTh4VgcsCEFAlSGZqdh9N0aZAQFZwsgCPwCAMwY1OU3MykjsiuW18BaJ+CrPq+8jGOMwkh65YTG7qZFxjn9+fW9WF+tL22sBLpQlLc5R2xaHT6Jo1wzk+RR70Hvq7FBKQEBAAVBKoZkWGqMJFIWETLDbPeILl40BALxVXW832y2cUo770sKBPSWoysjzyWdNFNEz8h6DAp8smlDc4qaqLDRGJpSF7OqKTCgBCkMqIslBInKy2crgHIbLZyaSwlgmc0rcphon47qFxkgCFfl+MSQiWVFBBtGg7L5AGPFOQ24mQy5uxHQTL26vdW1UenF7Ldo0A2/vrgeDOMcSFcd80dQKfOGyMVnH3WIc//HeIbxV3RmiW5jjtRIluOuKsfjcJVVoieooz/ehMj/Q43OpSBQBVUJQkc76YCLPyHsMGlSZJgd7pw1w5tyO1UqU4tOzhuMvW084DD0lwPLzhkGRKBraE6go8CHQzRLcJxFXz92wGP7hlT2OBHC67k0KiRJIJBkiIKl/D27jbyaNuW4yJCwr54xmAOAM0JNVLYbJYHKGo00x5DpEFud4s7reUR9lMQ4LwFu762FZDLdfPhaEADKhoBR4asNhrN2d1ItPlkuu3V0PALgrqWCaSVFAwYjCQI+8cJkKVdSA6q4xf7bwjLzHoCI1BDxhMrTHDehJ7aIUX1s8EZQQvLjtBAgl4Izj2pmVAIAb/22jPQj82vOG4StXjreHPHMuvPOmaALDCwMwLI5YwunFU0Lwj6/twYsZjTd//tipewOkDBB3aJUTIuaQNkV1DMv3Iz+gDFivn3OOhCm8dD05N7dDM7LyHYAIfegWg2EyEaZhzFXitzCoguVIqnRVnaKbDG/vbcDy8yqFrpVEoCgS3rLnAneSMBneqq7H5y6psnMxcnLodlCRsgZzZ5ISPvQr9JwMCHHDM/Iegw6SNMyyRGElS+hSyJTi/qsn4e4F42yD8+S6g3gpIwzw109OwrQ4vnzVeFiMJ2vr64R3zjnmjQ7ikbGWwzuPJQz8ZduJrHCCZgrdm7vmjUXYp4CQTk8+NZzEZO4rgIeWTYZfkSBRAoX230HbtjFPGfa0HIbJGH6eVPVM3USXTa/AnZePhQWeU7OdM8DgotHNsjgSpoWSPBW1bQnH6yT36Y8OKCFojiZQGFSRl+9PDgTJMTaSAh2agfKwDz5ZctWJT/9cn0zhUyT4ZdovZ0R7Rt5j0MGTIZqUnrfFuB37Tf2kg6qMqmIZsYSBF7fVZkkaJEyGV3fV4fbLx+C/Nhzu1LVJet7vHI7i52/sw9eTY+QAoKFNy6l7QonQPRlRFABS3ZFiY0EJwRNr9+OVnXWOFcD/fnwcCdPC1xeLZh8CEVpSJApVlsR3kc5afZEAJsnvEx2XKfVVmvpvH9wkUsczkWbUc5UqmpZIlr6ys85x8xMyEhx3XTEWccNCc0RHOCByF5bFYHAOnnZKLMbx2F+rsww8IGrfGyLumu4pDIvhx3/bDUmiYIxj/qSynN4/58CE8rycVTOqTG2l2/7irXeFZ+Q9Bh2EECgSsVUKJUogUaHvnepeTP2vri2pe+MyB0QiBE0RXRikDO9ctzhe2l6LJdMroMoSOOdo10wkTPeBIgnTQlQzUNuKrA4qzRDKh5mqigmT4eXtJ3HD7JGuZZyUEshU7OupVPakjH5Nmw5/Y1SsKIj4vFSeQCIEMqV2WaGZNOwmE/mNmG5mhV5iuonDjTGYjKE05IMkEcR0S8j2uuzbm7vqoOkm3jvQZIfFLhtfgpVzRmWFqf740VGcaHMfqN0aN7roV4YdxzcYYCSXDe/sa8TwwoBrA1x6WWTqWvJJIq7uk/vvaioXnpH3GJQEFAmMW1nemkwp0nNgE8pDueuqGcfJ9njOGZmEEJxo01CRL0ou//zx8ZzDSTgHnt9yHDddNCppQMVsAxCC1pgBiRAYLmaKUjFrNFAYyHqOMQ6dcegWoFAKVe6ZsWdc1IgbDDlvSqnQi55cAaV/5/98cBRv722AlKxIuXJSOQzGsG5vg53QJgCunl6Ba6YPyxkWsTjHe/ubkn0M4vkNB5oAAKsuqrJfpxkW3j/YlHN/KCG4dFwx3j/UlFU5RZPWPzMilDAZalvjWDZjmKMB7rrzh+OhZZMRVGUx2P0Ub6D9Ec/IewxKxGARGYlkjXzK+KZix5ppiSoPg2HhlHK8tbve4a2rEsW8SaUoz/d3KVVbEBBTf9piOt7b35TTm+QQBuxTs4bDr0iwLA7Dgp2ky1U2yBiHP1nnLVFRItoS1e2a7tSHCy9bTCTqLjmY63sSpgjBGCYDy7En//3BUazf2+CYrfrG7ros48oBvL6zDpG4mTMswjiywjyGxbHhQBOunzVCqDoSIKIbydm+uc/DPQvGIT+o4K3qehCCZEimFDfNGYX7n93mWlorSxS3XTYG314+Fa0xAyMLAwgHzu0UpzOBZ+Q9BjUypYhZoiomkjBhuniUbo0u8yaV4pZLqiBRgvmTyvDO3kZH3F6hwBUTShGQJTzz0TG8t78RZo4EYgpKCNrihi1JazKO379/BOv3NboKpKkSwRUTS0EIQUtMx//bXIO1exvs5OWVk8rwuUtGg1Jid25GExaCqmQPtiDJ2DwlqYatzrg9YxyRhAndYHYYoyvaYgbWJQ18OrkKWziADw83YfboInx8pNXuPAZEspTneC9NioKVhoIgVAzl6IrFUyswvDCAh5ZOxjcWT0RTtDOMFOtKkoBzTBmWj5BPRmVB9kppsOAZeY9Bh2kxRBImOjQTMd2yDaBfkWAQDoszh7HPbHQpCqnwpSpzLI5bLhGhg3f2Ntix4wsq/fj8paPxPx8cxcYDzd0aeEAYFYUSdMQNAMBftp7ApiMtWUaTJuPjF1QVYf6kMpxs1/DytlpsPipemwrrvL23ATHDwg0XjHC8X6IEvrQYvmZYaIsbKAgoUCUK3bRgMqCmSUPMH3HcBChJS9ZSAglEJK0ZQ317okuP2g1CCK6cWAZFovjwULN9/OaMLsKmwy2uCVvGRfz/eFsMcjIMNX9SmesNZmS+goev6exBUGUxAU6RKGRKUBBQcNOFI/H85hpHR3RAobjpwlFDYlrc4N9DjyGDxTjqOzS0x03bsGeiyAQKJHCZw2LJShHGAC7i+OmxbwoCRQICnOKeeeOw5pLRaIomkO9XUFdbA8NiduiiOxSJYHZVEUDEqMGEaeGjwy2O8k77ewnBN6+eiLBfAYGoUNl0JPu1hsXx4aFmLJ5ahoTBkR+QRbUH6Twez206hg3JxKbFOC4cXYRrzhsGiRKYnGcllNNJefopQ2yY/JTVEjnnKAwpuOGCEbj2vGFoj5v2dlICbDzQ7DhTBMCl44pRkucHJbCTv6kb7fq9DSAQK4CrJpfhuvEyZEqRp8pQFQqZZsfRv3/ddEiE4JlNx+xV0E0XjsJ3V0w7pX0ZqHhG3mNQEEmYONmm5YxtZ0IIgSwlG11A00SrhCFLdzDjJrM9/NElIQBAEyVo7IFnm/KQZ1cJ4wqIZKfo3nR/L6UElgX4JAkSARo0UQHkdkOwGMejL+0WPQGM49JxxbjpolEAYBt4cRMS7918tAUmY7hiYmm3w8gNi0MzLEQSpq21ct6IfHxyvN2xLYTANeFMIPabMfF8yCcj36+KFQIlUCWa9V5CUg1FznS3IlHcecU43HrpaLRrJkpDPuQHZBw+fBiRhIlowoJfSTUiSQgonV2mskTxfz89Aw8tm4K6ds2WmhgqDJ099Ri0JEwLJ1rjvZKVTUEpgZpWGseToZp/T85+FbF6jnmTynDdzOFoiJkoCeXutJQp8ODSSeCMIJz0XC3G8cK2E/jgUDMoQU4jyzlHSZ6CVF9NfkDuMnkJAFbSI3//UDMIIVg2vQLv7W9y9f43HWnFtpo2MMZxUSOxPft0LMbx+q46bDrSYodYzh9ViKunVIASgm01bZ2PjywA5xwf17Q5DPb04WHMm1CKxmgCYb8MvyxDlTkUSawq3juQXQ3DOPDOvibcftlY5PllSMky0c6yRQXl2TOKkhPCLEeCVaYEIZ8s/qeK/44ry3M9joMZz8h7DHiiCeu0DLwbhBA8+c4BvF7tbIJav7cBhslw6TCKkE/BpeOL8f7BZkfIRpEILh5bjNI8v+MzX9h+Ah8ebnb1yDPf65MlWBwwTCGde8GoQnx8rLXL9wKd1SnD8v1dDjRJbe+mIy3QTAuLp5bbdfISpXh1x0lstb9PvHZ7TSsUSvCZ2SOwfOYwdGgmwn7Zbgi69vxKNLQn8O7+JlTXtmNXbQd2nOiwG7EuHF2Ea2dWwmIUTVE950pGogQJy0KZ6st67lQwGUdb3EBb3ACBkKQO+SSEfHK/ncd6JvCMvMeAJ5fe++kQ1y28uiN7uLdhcWw82IRLKkqhyhQ3X1QFSogd90419NxwwUhQIqpeOICEYeGDg005E7SqTME5x8VjirF4agWao4YdeiIQsrYMHNuOCQ/a4rnj4ybj2HKkOWfVS+Zrdxxvx8VjigEAUd2EKlFsOdaa9flGMjdw5eRyBH0UpXlOI+yXZWyracCeug5HWXyqVHLz0Rb4FIpVF1fBp9DcXbKMgYIgrosQTF/UqXNwxAwTMcNEQyQBmVKE/TIKAsqgN/i9MvKapuHBBx9EU1MTQqEQfvKTn6C4uNjxmi9/+ctoaWmBoijw+Xz4zW9+gyNHjuBb3/oWCCGYOHEi/v7v/x7UZaSah8epEFAllOb50BjJbnnvLU3R3J2wlBB06MIAS5Rg1cVVuP6CEXYFi9NoiNDE85trcht4ieDu+WNRVRREJCEauFKx6XSumVGJRVMq0KEJz/SJdQdybv/BxhiKQira4ka33j/A8fbeBhxoEIOuu0quEgKcbI+jJKRClZKaLaqEkCLD5AybjjTnTETbNfAXiBr4y8aXpOUMBIpEcNn4EiQshpPtmqjyAWAwjsoCPwJ9NDjdZAwtMR0tMR0hVUZRSO22VHOg0qu9+sMf/oBJkybhvvvuw8svv4wnnngCjzzyiOM1R44cwcsvv+y4C//oRz/C/fffj0suuQTf+9738Oabb+Lqq68+vT3w8ABQmueDT6aobdP6JHRTEvJ1EQfnCKtOA5xK+Lnx3KZj+PhYa87v4gDGl+VBpRRxwwJLu7HoplBvDCcnCKkyRUmeD02RBCiyOzntbQTQGtNx/qhCbK9pAyHIaXwtBhxsiNrSvF1hWhylIR/8ametf0QzEdUsRBNdNy0Bzl6BlReKBHHmKij1uMU4/rjpqOP5RVMrcN/CCX2qzhnVTXsFUxRUURhUBnyXazq9MvKbN2/GXXfdBQCYP38+nnjiCcfzjY2NaG9vx5e+9CW0t7fj7rvvxlVXXYWdO3fi4osvtt/33nvveUbeo88I+4UX3RLV0RY3cjbB9ISAKmHpjAq8liEa5pMprpxchp42RmqGleWtpiNT4LLxJfYNoizsQ1y30K6ZeHl7LbYea7UN3KxRhVgyrQKUElFe2U3JukQpLhkrwj8dmoH3Dzbjk+NtDs9eIuKG0L23n4SI+vxlM4Y5HubgdoVPV6R3CXe3CnKrDnqzug6mxfDNqyf1uYaMbjHUdWho1wyMKAz0S0XJ3tCtkX/uuefw29/+1vFYSUkJwuEwACAUCqGjo8PxvGEYuOOOO3Drrbeira0Nq1evxsyZM8E5t++Qbu9LUV1d3aud6QpN087I555NBsM+AGdnPxjniCQY2hMWMqcC9pQloyja2wLYcDRmT5SaOzKAFWNlmHoCsaaTiOoWdCu3rW2KmV0OHZxc6sNlwyhqao47Hn9lbzu2nYwnQzzi07cebUEsFsPlo0P2e/c0JnLK7FqMId7eAjMqtmB2OUFCU7GnMWHvz5hCBUfaDJg9tPGcAx8fbcGMYhFayWRSiYq9TQnX0JRMgZkVfjTWnXT97Mb2zn/rJnPtIjYsjrf31OPSCqAyX4WeSODgwUM92/hTYDcBhoWFfs3Z4Ez+Jro18itXrsTKlSsdj917772IRqMAgGg0ivx8Z01TaWkpVq1aBVmWUVJSgqlTp+LQoUOO+Lvb+1JMnTrV9fHTobq6+ox87tlkMOwDcPb3I5Iw0RY3EEvkbnHPxbcndA4LKQn57JjwwYOHMG6cmB7EWLJ8T2dZbfSlhgW+udn1sxWJ4K6rpmSFeTTDwvZ36rMMnMmBfc06brl8AighGFHJ8NdPavHRkZasOnWZEswaVYiRw50e9w3DOkNA8fYWlJeX459e34tT6WLlAHzhIpSFOxOvlBAEVAlTxhK8sO0E3tvfmEy4wla2TIViehJqqWvXINEm174HiVL4C8sxbkyR4zz0NUFFRlVJ8Ix8diZ98ZvYvHmz6+O9CtfMnj0b69atw8yZM7F+/XrMmTPH8fyGDRvw+9//Hr/+9a8RjUaxb98+jBs3DtOmTcMHH3yASy65BOvXr8fcuXN78/UeHqdEnk8MTuZcGONU80wuBcZMAqqEkWruHzu167EBQE0Kn1nQTAaFki4TjG5x/LZ47ti20HXhqMgXBvYLV4zFzReNwh8/OoaPj7ZAoqJq5cIxxVg+fRiQ1IjhSeVJzkX+QJUp6qIEqkwxa1RhWrmkIBXGcbsnMg58fLQVN104EpIkyi6VNGnP9BCMX6bQTHbKVSwFASVnboVxjvFnod5d6+H10d/plZFfvXo1Hn74YaxevRqKouDxxx8HAPz0pz/FsmXLsGDBArz77ru46aabQCnFN7/5TRQXF+Phhx/Gd7/7XfzTP/0Txo0bh6VLl/bpznh4dAUhYohIUJWBsFBujCUsRHSzV15+LlIJ0nDy779bMhn/tu4gXk82VVmM4/IJpbhxzkjX93dn4AoyEgJBn4w7rhgLzajKUeHjDovIqCzw49a5oxFSJWw46EyAmkxIAbvx8bEWrL5kVM7vSU9EF3S7Je7vd7s5qjLF0mkVKAydebXIwuDgUKTslZEPBAL42c9+lvX4Qw89ZP/7//yf/5P1/NixY/H73/++N1/p4dHnKBJFQZCiIPljTpgWNINBMyzE9aRE8SmEMXJ+j0xx36IJuGveWEfYJ6XXblmi5j01kEMip+79A+4VPuniZJnPkaQIGaUEqy6pwvWznQnQE61xbHTpSgWyFTV7Slfbk8lNFwoV0Hf3NYmOYw4snV6BLy0Yf0rfeaoQEBSFFJTlnV4zVn9hcBaGenj0Ap8swSdLtqecGkatGZ3G/3QMf2bYJ+Xxu/HgUuH9v7azzpY/vnJyGVZdLMoLTYt3ufLIFCdLL0/MFRPPvEkUh1QxGMQls+u2ouiK7rZHIiQ51pDCJ1EoslCffGjZFNy3MDsncqYIKBLKw31Xj98f8Iy8h0cOCCFZhi81PzZaL6M87E+boGT1vAyxB8gSxb0LJ+DOK8bmNHCcCyVNk4mxfJxxWMm4+1PvHcJGW25BbNfGpIFddXFVzglW6XTXsOTmiafmyqbfRmRK8N+bj2Ztz/sHmxH2KfjqwvFd1qV3lxM5XfyyhLBftnsRBhuekffwOAUIIVBlgqBCURxSHc9lDrjWre4HXXdHVwauU0nTaWzjuoW39zRkSTLolhAF+9qiiQioEqw2GaOLg+A8NcCjU32Tg4OA4OuLJiHPdwiv76qDRMUUvyXTKnD3vHFifKG9LchpqOO6lTV0BRAj+F6rrsOd88aeVc9ZpgQ+WUJQlQatYU/HM/IeHn1E+sDwTFhSt96wOEwr+V8mhpekBmT3lchaV5IMEiFoiiYwUg3aMflO3I20Wz7hTGzPmUDIFkvwyZ3/zZSLGOx4Rt7D4yxAKYGPSuhKHiW1EjCZuBFYTCRkUxOqGE9q3rOu4/FdSTJYnKMkdOoJxdMJmZyJ7UlBgeTA7dT/CGSJCl0dmfZ5V+xAxDPyHh79hNRKoCdw3lmRk278U39/atZwvLTtBLQMSYZlM4Yhzyf3SKGyr+hKImLJ9AoEVEkIkSUliSVKOscPph5P/ZsSKJJ4jUIpeIs6JDXiTwXPyHt4DEBEPF7E5N348Q3nIaRKjpF3NydH3qU0WaxmBZPKw2DJRqlUuCg9Lp/6O3VP4Jyn/RvOfi2S2jbxT0JI8r/AY9efh3y/gj9trgGlBIxx3HjhKDyyfAp8ijSoBMH6G56R9/AYhPRk5J1dJ9+luk7f8f995jx8Z/nUITmC71ziHWUPj0FMfxt519+2ZygwtNLMHh4eHkMMz8h7eHh4DGI8I+/h4eExiPGMvIeHh8cgxjPyHh4eHoMYz8h7eHh4DGI8I+/h4eExiPGMvIeHh8cgplfNUJqm4cEHH0RTUxNCoRB+8pOfoLi42H5+/fr1+PWvfw1AtEFv3rwZL730EhKJBO655x6MGTMGgBgjuHz58tPfCw8PDw8PV3pl5P/whz9g0qRJuO+++/Dyyy/jiSeewCOPPGI/P3/+fMyfPx8A8Jvf/AazZ8/G+PHj8dxzz+ELX/gC7rjjjr7Zeg8PDw+PLulVuGbz5s2YN28eAGHQN27c6Pq6kydP4i9/+QvuvfdeAMCOHTvw9ttv43Of+xy+853vIBKJ9HKzPTw8PDx6Qree/HPPPYff/va3jsdKSkoQDotZ9KFQCB0dHa7vfeqpp3D77bdDVcUEnZkzZ2LlypWYMWMGfvWrX+GXv/wlHn744az3VVdXn/KOdIemaWfkc88mg2EfgMGxH94+9A8Gwz4AZ3g/eC/46le/yrdt28Y557y9vZ1fe+21Wa+xLIsvWbKEx+Nx+7G2tjb73/v27eO33npr1vs2bdrUm03qll27dp2Rzz2bDIZ94Hxw7Ie3D/2DwbAPnPfNfuSynb0K18yePRvr1q0DIJKsc+bMyXrN3r17MXbsWPj9fvuxO++8E9u3bwcAbNy4EdOnT+/N13t4eHh49JBeJV5Xr16Nhx9+GKtXr4aiKHj88ccBAD/96U+xbNkyzJw5E4cOHcKoUaMc7/v+97+PH/7wh1AUBaWlpfjhD394+nvg4eHh4ZGTXhn5QCCAn/3sZ1mPP/TQQ/a/r7nmGlxzzTWO56dPn44//vGPvflKDw8PD49e4DVDeXh4eAxiPCPv4eHhMYjxjLyHh4fHIMYz8h4eHh6DGM/Ie3h4eAxiCOecn+uNSGfz5s3nehM8PDw8BiRuPUv9zsh7eHh4ePQdXrjGw8PDYxDjGXkPDw+PQcygN/Kvv/46HnjgAdfnnn32Wdxwww246aabsHbt2rO8Zd2jaRruu+8+3HLLLfjiF7+I5ubmrNd8+ctfxqpVq7BmzRrcdddd52Ar3WGM4Xvf+x5uvvlmrFmzBkeOHHE839+PPdD9Pjz66KO44YYbsGbNGqxZsyanGmt/YNu2bVizZk3W42+99RY++9nP4uabb8azzz57Drbs1Mi1H//1X/+Fa6+91j4XBw8ePAdb1zWGYeDBBx/ELbfcghtvvBFvvvmm4/kzdi5OW/qsH/PDH/6QL126lN9///1Zz9XX1/MVK1bwRCLB29vb7X/3J/7zP/+T/+xnP+Occ/7SSy/xH/7wh1mvueaaazhj7GxvWre8+uqr/OGHH+acc/7xxx/zL33pS/ZzA+HYc971PnDO+apVq3hTU9O52LRT4sknn+QrVqzgK1eudDyu6zpfvHgxb21t5YlEgt9www28oaHhHG1l9+TaD845f+CBB/gnn3xyDraq5zz//PP80Ucf5Zxz3tLSwhcsWGA/dybPxaD25GfPno3vf//7rs9t374dF1xwAVRVRTgcRlVVFXbv3n12N7AbuhvO0tjYiPb2dnzpS1/C6tWr+5VHnL7ts2bNwo4dO+znBsKxB7reB8YYjhw5gu9973tYtWoVnn/++XO1md1SVVWFn//851mPHzhwAFVVVSgoKICqqpgzZw4++uijc7CFPSPXfgDAzp078eSTT2L16tX493//97O8ZT1j2bJl+PrXvw5AjEWVJMl+7kyei14JlPU33AabPPbYY1i+fDk++OAD1/dEIhF78Akghp+cy0lVvRnOYhgG7rjjDtx6661oa2vD6tWrMXPmTJSUlJy17c5FJBJBXl6e/bckSTBNE7Is97tjn4uu9iEWi+Hzn/88vvCFL8CyLNx6662YMWMGpkyZcg632J2lS5eipqYm6/GBch5S5NoPALj22mtxyy23IC8vD/feey/Wrl2Lq6666ixvYdeEQiEA4rh/7Wtfw/33328/dybPxaAw8itXrsTKlStP6T15eXmIRqP239Fo1HGQzzZu+3Dvvffa2xiNRpGfn+94vrS0FKtWrYIsyygpKcHUqVNx6NChfmHkM48vYwyyLLs+d66PfS662odAIIBbb70VgUAAADB37lzs3r27Xxr5XAyU89AdnHPcdttt9rYvWLAAu3bt6ndGHgBqa2vx1a9+Fbfccguuu+46+/EzeS4GdbimK2bOnInNmzcjkUigo6MDBw4cwKRJk871ZjnobjjLhg0b7OVfNBrFvn37MG7cuLO+nW7Mnj0b69evBwBs3brVcWwHwrEHut6Hw4cPY/Xq1bAsC4ZhYMuWLQNuCM748eNx5MgRtLa2Qtd1bNq0CRdccMG53qxTJhKJYMWKFYhGo+Cc44MPPsCMGTPO9WZl0djYiDvuuAMPPvggbrzxRsdzZ/JcDApP/lR46qmnUFVVhUWLFmHNmjX4/9u7YxQJYTCK4w9htLfxBB7Cyso6hRDFwsYTaOUJPIJ4D6+gF7LQMltMs8sWM80im/n/TvC+BB4kENI0jZxz6vteURTdHe+HV5+z5HmubdtkrVUQBBqGQXEc35z6qSgK7fuuuq7lnNM0Tf9q7aXXMxhjZK3V4/GQMUZpmt4d+S3ruuo8T1VVpXEc1XWdnHMqy1JJktwd723f5+j7Xm3bKgxDZVmmPM/vjvfLsiw6jkPzPGueZ0nPE/x1XX+6F7x4BQCPfex1DQB8AkoeADxGyQOAxyh5APAYJQ8AHqPkAcBjlDwAeIySBwCPfQEk5vyf9UCjfQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm16, Xmoon, label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here the mixture of 16 Gaussian components serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n",
    "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n",
    "For example, here are 400 new points drawn from this 16-component GMM fit to our original data (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vvPMO8vPzce+99+L8+fOwWv1fQVevXo3nn38eO3fuhNlsRk1Njd6fjykNTXY4e4PD2jkAM8bm+f7efPAs3F55gSfbOEERr0Qk0S3yBoMBGzdu9Ns2evRo3/8nTJiAbdu2+e2/+eabfV43iYpc1CMPYK/NjjtG5soGxQDXXR7pgU5tKOKViDSU1kAjSknExAuprIXXQJfHRIVmoPKo6Z9wpcQgCBYU8aoRNQFEdocLU+oaMWNsXtIWjAhHlalkRm3/sLyvKFCNCBck8hpRG0Bkd7iw12bHwsnWsFRJijco54o8avqnocnOTENBgWpEuCBzjUakfKVZuNz9OHymPSlMM4FQzhV51PQPK2UxByTF2x4RH5DIayQwsEgpyCBZRY9yrsjD6p8hZpOvoAvr3tFb+pEgpCBzjQ7EBaalQtrF8IBi9slEhApUy8NKG+3s8/js9LLH725JunuGiA0k8iEi9TAHkoyLklJpkZNlvSEcSPVPVkaabCZRMW4vj+p9rZFtJJESkLkmREqLrPjswhW8f+Ki7OwsGd3iKOeKPIH9c8vaA5qOl8ocShBaoZl8GDh8pl2VHTVZ7fOEOvSsVyTT2x8RG0jkw4Ba8aZFydRGjWkvEHJJJUKFRD4MqBFvWpQkxHZ6tdDbHxEqJPJhoKqkACajf1iLgQOGZppoUZLwQ/DMUiv0OZmmCLeISHZo4TVcBBjljRyHDfPGkbATklSVFGD17hb0K2Qp7erxoKHJTvcRoRuayYcBqZTCbi+PF/eTCxwhzWcXrigKPDBwH5FdnggFEvkwwLKbdnS7yTuCCKKhyY73T1xU/XmyyxOhQCIfBuQWXmkWRgTCylnDgryyiFAgm3wYqCopwMr6Zsl9NAsjAtFyT4i9sih/f/IhXFO7wwUjx6Gf52EN87WlmbwGGprsmFLXiFvWHvDLR1NaZEWOWdoLgmZhRCBy94TRwCHHHOyVRfn7kw/xNQWAfn7g/S7c15Zm8iqRKtO2sr4Zq3Y1g+cH3CVNBs5vAZZ84wkpWOmqLelG/McPpV1tqYJU8iFXZS6c15ZEXgUNTXas3tXiG2nFCJs6uv3zjAzNNKWMCyWZEbQRmK5aTZ9R/v7kQ+nahevaksgrIMzgpQRejm+7UyO5FBWi1ofW5G6s/PQGjiM/+gSFdU3F+8MB2eQVUCrczcKL1PCsYZkRKE1ueGHlvennebLNJxiN5zoxpa4RdoeLWf4xnKZe3TN5r9eL6upqnD17Funp6aipqcHIkSN9+2tqanDy5ElYLBYAwLZt2+B2u/HTn/4UPT09GD58ODZt2gSzOb4XJkN5ZUqFV2nWOTpcbpphhhGhH6XMhmSbj2/E5sycTBOuutwQygrwGCj3yAMR867RLfKHDh1CX18f6uvr0dzcjLq6Orz55pu+/a2trdi+fTtyc3N922pqajB37lwsWLAAb731Furr6/Hwww+HdAKRRumVSunYZEeuf0h4wktpkRWrGK66dofLV1aQ1kXih0BzZuDaHTAg8NYcc8RqQes219hsNkydOhUAMGnSJJw+fdq3z+v14sKFC1i/fj3Ky8uxZ8+eoGOmTZuG48ePh9L2qKAnPSww0LGp4Fkjd46p8CYTLQT3XdbKEAeQe2UcotbcG8lnRbfId3V1ISsry/e30WiEx+MBAHR3d+Ohhx7C5s2bsX37dnzwwQc4c+YMurq6kJ2dDQCwWCzo7OwMsfmRJ7CMm5FjWdH8GZIi2QNLi6wYyjjXVHiTiQaB/tSBCK/7Ylzufqysb07K+sKJRDzUmtBtrsnKyoLT6fT97fV6kZY28HVmsxlLly712dvvvvtunDlzxndMRkYGnE4nBg8eLPndbW1tepulisZznfi17Qoud59DniUNy4qHYuaobObnCzKA7fNv8h279fhl9IpqdQ4ycrjvH7Jw6P+6fNs7ut1Ys6cF9q/sst+tl56enoj3k1qWT86R7JPK8VnMNsZT+/UQzfbXfniRORscbknDJaeHeazd4Qq6D6nvo0eewvURmHRjWsTOSbfIFxcX4/Dhw5g9ezaam5sxZswY376//vWvWLlyJRoaGuD1enHy5En88Ic/RHFxMY4cOYIFCxbg6NGjmDx5suR3FxYW6m2WIg1Ndrxx4oLvobnk9OCNE1fwtduMw2fag2yagYsmPA/09vNBiySbD571Ezlg4HMfnOrCk3PuDPt5tLW1RbSftFBYCFhHaPOVj6f26yGa7W93npPczgH45IUSn6cGi8D7kPo+ejw/d7Bk4FsgzX/3hHxONptNcrtukZ81axaOHTuG8vJy8DyP2tpavPPOO8jPz8e9996L+fPnY9GiRTCZTJg/fz5uvfVWPPHEE1izZg127dqFoUOHYsuWLbpPSC8slz9xIW7BpvnZhSvYa7NLLpr08zw4ADPG5skuiKWKXVrO71sqWKogI8oNTGByMk2SC3bCK35VSQFW1TfLJj1Llfsw3hCeiRf3t0peQ4FIXh/dIm8wGLBx40a/baNHj/b9f/ny5Vi+fLnf/htuuAFvv/223p8MC6zOlLJp7vz4S9kgKB7A+ycu4o6RuUwvk1S1S4sTL4ltxsIAuuLuXCTIZCymNDTZ0dUT/LpvMnJ+i95KoXqpeh/GA8IE6HtrDzA/E5c2+URFi0ukmihXHgNvB1L5SFIld414pj7EbIK73wtn3/V+kBpAd5zswJNzotvORESqIA0AWNLT/BKXyZEq92G8Y5XRHmdv5CqApVzEq5RLpDp/GTZfOVxBXjipUtc1MDuiw+X2E3gW7SoWowj2m+e3roFXfyUXvRyzKSXuw0RAzh3b4XJHzO015Wbyws1e++FptDs9GJFjxoyxeX62d60YOA63rD2QkkEoetM+5FlS7tbThZIZUM6W+9riSSl1L0YTPUn5xNoj5XETqcjllHzSSousKMi46reafcfIXMXFERaBeaCF30gF9C4YLSseGuaWJCestMTdfQOv96xBwJpjTpl7MNqEkpRP0J7ZO85JrqNEYgE25cw1LEqLrNCYaFISYTROFfQsGOWYTRGJHUhGBDNgYFGaju6B1/sZY/OCTABkg48scrn91cJ6biKxAEsiL8LhCk964FRyV9Oa9sFk4FD9g3ERbFHyUVpkhWVQ8Eu3y92Pw2faU3ItKJaEI7e/1HMTqcE5Jc01kSaV3NUCC2BIedeIycoY8Appa7sazWYmPHLCojU3PREa4XCX1lM4Ri8k8iKGMoJOtJCKr8pSIsPyCXakSDGVcENxGPGDkru01KIscF3Q8yxpeH7u4KgNzikl8uLOFzoa8J+FGg0c+kV+ySYjB0t6GtOUI+z/1uVOSe8aMeL+FdI+BEKipI9UjsOIN+Rm4VKLslV7WgAevniHS05PVB00UkbkAzv/ktMT1PmCkHPcQO1Wq2gUlvJwSKU6rkoE9q+UwJMo6Sear/eEMqxZuNSirLs/+FmIZqGXlBF5tZ0PDAi8OC+N+DvoAZOG5S9v5Dh4eZ76LAyQ7T3+0bL4Gi0HjZQRea0dKs5LIzxc9ICxYfWvl+dxvo7yFxCpgZa0KdEyXaaMC6WeDuUBPP/bzzGlrhG3rD1ABRhkiKbfL0HEK1KukSYjB5PBP3mKycChu88TFV1JmZm81MKVycj52eSl6HZ70X1tZE7FiFa1qF0YbGiyo3pf67X1j3O0rhEFAr09KsdnUQbQCCFeO7Ffc0Bw9/MYeq0WxbcuN7LSOfT0X09dHmldSZmZfGACseGWNGx+cCIW33mzpu9JtYhWtahJ0NbQZEfV7hY/T6WObjeq9rTQG1KECEwgZ3e4sPX4ZervCFJaZPXN6AUHhI5uN3o9Xry6eBLMJmPQemAkdSUlZvKBM5lXF0+6lrvGqqtjUymiVQtK6xastLnufj5qngaphtSCeC/1d8RhpT5YvauFmcI8UrqS9CLPSiYkFK3Q07FkZ9aGuIAICxo4IwOrz6W268msSATT0GRn9rtcjYpI6UrSizxrRBWKVmhZDQeCK/IQ8gQOsixo4IwMrKA0I+e/EBhKZkViAP/1Jm1EMoYkKWzyDU12pgcMa4YoFK3QmmBLsc4a4YeafPM0cEYO1syxn+f9npNwZFZMZYRBUo/ARzqpXMKLvNTCkrjCCmuGKBStCFwwDJzhBOL28nTja0DJDDM004TND06k2WKEsMq8IYmfk3BkVkxl9BbPseaYcWztzIje/wkv8kozEFZKT3HRitIiK46tnYnzdXOwZdFExZk93fjqkTPDcACa1t9PAh9BZozNY5a3FD8nFOcQGmomM7HK+5/wIq9mBpJhun6aQs1LVtEK8cyeBd346pkxNo+5j/oxsjQ02bHXZpe1MArPSTTzmycjcvey2WTEhnnjYpb3P+EXXuVSsEot+vV6vIrfKbgCSh1PN742Dp9pZ+6TGwCI0FFjQhDEiRKghQarTGNgsN9ALYU2v9KjkUaXyHu9XlRXV+Ps2bNIT09HTU0NRo4c6dv/61//GgcODOQTnz59OlasWAGe5zFt2jR873vfAwBMmjQJq1evDvkE5CIt5Uw52+ffpPjddOOHjtxrrNwAQISOGrOieMJC+Zn0E89aoUvkDx06hL6+PtTX16O5uRl1dXV48803AQBffvkl9u3bh927d8NgMKCiogL33XcfzGYzxo0bh1/84hdhPQG5zl1V3yx5jBabOt34oSHnokprG5FFyT3YbDLQvR1G4lUrdIm8zWbD1KlTAQzMyE+fPu3b953vfAfbt2+H0Thg3/N4PBg0aBBaW1vx97//HUuWLEFGRgaee+45jBo1KgynwO5c5k3OAY3nOil/RxSoKinAqvpmSbuwYCqgIJzIMGNsHt47cZG5P0OL6zCRsOgS+a6uLmRlZfn+NhqN8Hg8SEtLg8lkQm5uLniex8svv4zbbrsNt9xyCy5fvoxHH30U3//+9/HZZ5+hqqoKe/fulfz+trY2fWcTQOX4LLx6zIVAMzzPA//5x3b88pPfo7PXizxLGpYVD2UuxsYjPT09YeunSFKQAUz8ziA0/7/eoH2TbkzDzw98gq3HL6P3Wi4Pu8OFNXtaYP/KHtfXIxH6/3cnv5Td7+h2x/05SBHPfd94rhM7Tnag3elBVjoHjuNwtdcLAwd4+YGcWZXjswBEr/26RD4rKwtOp9P3t9frRVra9a/q7e3F888/D4vFgg0bNgAAbr/9dt/s/o477sClS5fA8zw4Cb/0cC1KFBYCv/rsfyQDFHgAV3sH1P+S04M3TlyBdUR8vm5JEe3Fm1Bo/93Xktub/+5B89+7fAIv0NvP44NTXXhyzp3RaJ4uEqH/O/vOye7nASz/3dcJ9+YUr33f0GTHGycu+NYBO/t4CNGTQsqmS04PXjvhwGUMRk3p+LD+vs1mk9yuy4WyuLgYR48eBQA0NzdjzJgxvn08z+Pf/u3fUFBQgI0bN/qE/Y033sCOHTsAAGfOnMFNN90kKfDh5luVEWgU3Rc55NxcWfvsDhdlStSBOPpbDYHBg4R+qve1qg6Iev/Exaj1ua6Z/KxZs3Ds2DGUl5eD53nU1tbinXfeQX5+PrxeLz755BP09fXhj3/8IwDgmWeewaOPPoqqqiocOXIERqMRmzZtCuuJsNCSm4YWAiMD6xoYOA7ZGewi6ZQ7RRtq8wQFEs16o8lKQ5NdU0oDHojvGq8GgwEbN2702zZ69Gjf/0+dOiV53FtvvaXn50KiqqQAVXtamPVcxVBwTmRg+RD38zycfR6YDJxkCmISH23oDa0HaIITKnqsAFoSI4ZCwgdDKSEIBMvDQ4CCnCKHcA2kcmkLVXOEKjmBROtBSAZCEWqa4Ggj0CNMz30aeWP1AAmf1kAtcgIfzRDjVKW0yAovIyNiR7cbcsszZC9WB0uolcSEJjjakEqKqEewo5XQNiVEXu5VKhpZ4IgB5GaLMrUUaEFcJay02VJda+S4qOdQSRakzGLxnIE86c01gPxrLM1gogfLNq8EmWzUIQj1i/tbmeYvAS/P43zdnGg0K+kI1/rF0ExTWL5HiZSYybNmkDlmE81gooiQ4VMrSjn+ieuUFlmRma48dyMbvH7C0XcmI4cN88aFoTXKJK3Ii/2FO5zB0ZYA4HC5gypJEZGltMgqm8ZZCrm6mEQwamaalAFUP6y0zHJwGJi5cxiIeo1moZykFPnAhZFuNzu9MAWDRJ+qkgIMMqqfnWsdFFIdNTPNvTY73fM6CawmJ6xr5JjZ5hceQI/bi1cXT8KOB/OjakFISpHX6i9M0a7RpbTIiqfvuUH2oRAgzw/tVJUUwKQwiNI9HxrianKC40b1D+TNL7Hq86QUeT0LIxQMEl1mjspG84b78driSX4zoofuzo9J9ZxkorTICosKu7zd4SJzZZgxGuQH11joTFJ61+gJTqCFqNgQrzm4Ex21OZsEcyVA6SP0IgRGqdGcWOhMUs7kWf7CLMgkQCQLgsOBlqVqMt3oR7z+p0SsdCYpRT5wYSTHbPKtbAsmgeGWNDIJEEmFFsEJhMyV+lC7/mfkOCycHJu31qQ01wDKZoB/KUjD2Z7B2HzwLFbVN2PzwbMJl1ebIMQoCY7JwMEySDrrJ5kr9aF2cOzneey12XHHyFwUZES4UQEk5UxeDY3nOoPyT5ArJZHIKAmO28uD4xDkvkrmSv1oGRzJuybK7DjZETTrIdtk/CEOaiNPEHnUCI6j242n77mBPJjChNbAKPKuiSLtTo/kdrJNxg+BRTDIE0QeNbmBcjJNmDkqO65LKyYSwn0YWIie5W1D3jVRJM8iPb6RbTL2CLP3lfXN9LalAbHDAYuuHg8az3VGsVWpCWuGHwuzWErM5MUJ/nMyTeB5wOHygIN/ilCyTcaehia7YiUvu8OF7609AOu1WRPN6q8jdjiY9GJwEXu3l8eOkx14khJQhgWpt82V9c0YmmnCwslWHD7T7jfDLy2yoq3talTbmPQiH3gRxClYecAn9DlmEzgO5GkTY17c36qqVCMw8EBV7WkBQOYbKVgBUSxTJaEdlkdTR7cbe232uFjvSHpzjZJbmSDwvR4vOrrd5GkTY5TyoAfi7ufx4v7WCLUmsWGZHlmmSkI7cjEJ8WJaTHqRVxMY4nC5yfabwGgdGFIFll14WfHQGLUouWhosiuW/YsHR46kHtKFi6A3G3k8XKBUI8dskgzWIbTD8vwoyIiuTThZ2XzwrKK2xIMjh26R93q9qK6uxtmzZ5Geno6amhqMHDnSt3/Xrl34zW9+g7S0NDzxxBOYMWMGrly5gp/+9Kfo6enB8OHDsWnTJpjNkesENRfBbDIiw2SQnA3GwwVKNap/MA5Vu1vg9qofmqluFBupyO9oL/wlK0qTwHhx5NBtrjl06BD6+vpQX1+P1atXo66uzrevvb0d7777Ln7zm9/g7bffxiuvvIK+vj5s27YNc+fOxQcffIDbbrsN9fX1YTkJFnIXQRwIsmHeuLhxd0p1Sous2Fw2MSj9sFw9TKobRcQCuUlgPAWZ6Z7J22w2TJ06FQAwadIknD592rfv888/R1FREdLT05Geno78/HycOXMGNpsNjz32GABg2rRpeOWVV/Dwww+HdgYysFIOW3PM2D7/JhQWFvptFwIYjBznZ5OPhwuVSkjNPu8YmYtV9c2Sgk6Vo4hYIBV8ZjYZ40bcBXSLfFdXF7Kysnx/G41GeDwepKWloaurC9nZ2b59FosFXV1dftstFgs6O6WDMtra2vQ2y4/K8VnYerwHvSKXvEFGDpXjs9DT0+P3OwUZwZ+3O1xYs6cF9q/smDkqO+j7Y0lg+xMNre2v/fAic8Z+udOFnx/4JKrXKJH7P5HbDsRP+wsygBV352LHyQ60Oz3Is6RhWfFQFGRclTWJRbv9ukU+KysLTqfT97fX60VaWprkPqfTiezsbN/2jIwMOJ1ODB48WPK7A2fYeiksBKwj7EELTwMBCW1Bv7P8d41+AwIA9Pbz+OBUV9yFgUu1P5FQ035xEJucSaa3H3jt+GVYR0QvlWsi938itx2Ir/YXFkJzYFmk2m+z2SS36xb54uJiHD58GLNnz0ZzczPGjBnj2zdhwgS89tpr6O3tRV9fH7744guMGTMGxcXFOHLkCBYsWICjR49i8uTJen9eNVoqD7Fs+MJ2seiMoGjLiBIYxKaEu5/HyvpmPPfbz5FhMsLR7aZrRISVRH3+dYv8rFmzcOzYMZSXl4PnedTW1uKdd95Bfn4+7r33XixZsgSVlZXgeR6rVq3CoEGD8MQTT2DNmjXYtWsXhg4dii1btoTzXEKGZcMfkWOmZFlRRmsxdgGX2wuX2wuArlEg/iL1dcKIVDyQyM+/bpE3GAzYuHGj37bRo0f7/r9o0SIsWrTIb/8NN9yAt99+W+9PRoTAvDYmA+fnvid42UiJjrA4G+8XOREJV4wCXaMBElmk4oFEfv6TPuJVDnG5NB7XIie5a3ls4O8GpWTKIcJLjozLpFboGsmLFKFMIj//SR3xqoTUje/u52EZlIbmDff7bZcz5RDhpaHJzkyupQe6Ruz0HnrqwaYiap//eLTbp7TIaxmdWT6xFDAVfl7c3woNAa+y0DUawMhx6OeDO9XIUbywFIFiPWNsHvba7LLPf7yaxFLaXMOa4UltFxdkoLJpkSXUhGMGDnSNApASeLntqYxQ00Bc/7n+0y+xcLJV9vmPV5NYSs/ktc7OtbhjErGD54HzdVQVQ4xVJvqb8EeqpoG7n8eBz79G0/r7GUfFr90+pUWelaWPhDy2hJqJMtVt8FJ2YTI3qmNdwynmm6TSG2a8rtultLkGGBD6Y2tn4nzdHBxbO5MEPg6o/sE4mAz+tmKTgcOU0bmKx6a6cAV6jIntwmRulGddwym8d+Ki7uPjqa6rmJSeyRPxCesNS8m2STVf5e3CwiQmntICRBvhLUdIRNjP8777ZufHX6o6nnV/xatlgESeiEuk1j9W1TczP//a4kkxf5jigXi1C8cDgd4vwqKzUHxbDUrBT/G4bkciTyQMLJvn0ExT3D1YsSJe7cLxgN5UGWLsDhem1DXG1UxdiZS3yROJA8vmuWHeuBi1KP6IV7twPBCut5nA9Y6GJntYvjdSkMgTCQPFKihDfcQmEm8z8eAHrwSZa4iEgmXzjMdw8lgRj3bheEDKjTQcxPt6B4k8kfDEazg5EV8I98KL+1tDjqoWE+/rHWSuIRKeeA0nJ+KP0iIrMtP1zW1NRi4ofiMR1jtoJk8kPGrdBsmkQwD6zCscgM0PTgQQf37wSpDIEwkPy23QwHG4Ze0BySyCZNJJXVj3ixLCfZJo9wuZa4iER8ptEBgIdhFc3d4/cVHSpPPcbz/HlLpG3LL2AKbUNca9OxwROlUlBUFmFyXi3e4uB83kiYQnMJzcIJE7nZVQ1+X2+mZ1NLtPDYRrW72vVVUiPA6Ie7u7HCTyRFIgdhu8Ze0B3d/jcvejel9rwtldCW0I90ugZ5YUPBJ70CdzDZF0hPpq7XC5Ey6qkdCHOHiMRaLn3CeRJ5IOVmi/JT3Ybq8GcsdMboR0468tnpSUKSF0mWt6enpQVVWFb775BhaLBS+99BJyc/1zfb/00ks4efIkPB4PFi9ejEWLFsHhcKCkpARjxowBANx3331YtmxZ6GdBECJYKV8B6I54jPeoRiJ04jVVcKjoEvmdO3dizJgxeOqpp3DgwAFs27YN69at8+0/ceIELl68iPr6evT19WHOnDkoKSnBn//8Z8ydOxcvvPBC2E6AIKSQC+2XSytr4CBZRDyRvSsI9SRjSghd5hqbzYapU6cCAKZNm4aPPvrIb39RURFqa2t9f/f39yMtLQ2nT59Ga2srHnroITz99NO4dOlSCE0nCO2UFlmZNlYO0gKfDK/sRHhoaLInnMstx/Py5dp3796NHTt2+G0bNmwY1q9fj9GjR8Pr9eKf//mfcfTo0aBj3W431qxZg4KCAjz22GM4dOgQMjMzcc8992Dfvn04dOgQtm7d6neMzWZDZmZmGE5Nnp6eHmRkZET8dyIFtV89jec6seNkB9qdHuRZ0vCP3zXj0P91obdf9tYHMDCz//6YbHz6N5fv+GXFQ3HPCFPC9j/dO/poPNeJrccv+903g4wcnr7nBswcla36eyLV/u7ubkyePDlou6K5pqysDGVlZX7bVqxYAafTCQBwOp0YPHhw0HHffvstnn76adx555147LHHAAB33303zOaBWdSsWbOCBF4gGqXJEr0EGrVfHQ1Ndrxx4oLPDn/J6UHjuW6U/ePNOHym3Wd7ZUVAenmg8Vy33/FvnLgC3J2LJ+cURbz9kYDuHX0s/11j0MSgt5/HB6e68OScO1V/T6Tab7PZJLfrMtcUFxfjyJEjAICjR48GjR49PT14+OGHsXDhQjz55JO+7evWrcPBgwcBAB999BHGjaNiD0RkYSUvO3ym3a+Au5FjR0BKHb/jZEdE2ktEllDMLYlaWlHXwmtFRQXWrFmDiooKmEwmbNmyBQDw8ssv44EHHsDJkyfx5ZdfYvfu3di9ezcAoLa2FqtXr8bzzz+PnTt3wmw2o6amJnxnQhASsB5Au8Ply2tTVVIQFCGrRLvTE47mEVEk1JTUiVpaUZfIm81mSVPLs88+CwCYMGECHn74Yclj3333XT0/SRC6kDPFiIOdcswmyRB3o0SKBADIs1CweKLBeqt7cb+6CGepoiOJsChPwVBEUsNKXibG5e4Hx0EyEKbirpslty8rHhr2thKRhfVW19GtLsI5UUsr0nSESGqEB3D1rhZZk4yj241/uTsfH3x8UeRGyeOOkbm4Y2Ru0EyvIONq5BtPhBW1KYaFCGcp8U5EP3oSeSLpKS2yygZAAcAQswn1n37p5yfvcntRtbsFm8sm4tjamX6fb2sjkY8Vjec6sfx3jaqiUsWFYnIyTTAZOLilgiECiPfFVC2QyBNJT0OTHRzY6YbNJiM4DnBL+M27vTxW72oBkNiZCJOFhia7n6+63eHCqvpmrKxvhjVA8AMXWgPruuaYTQAguRYT74upWiCbPJH0bD54linwOWYTNi0YD4dMYed+nqdMlHHC5oNng3zVhb8C7elSC61iej1ezJ14k+Sajd3hwujn/hvrGk6Fre2xgkSeSHrkXr2bN9yP0iKr4syNMlHGhkC/diWbuvg6KZlchHgJVqrhfp7HeycuJrzQk8gTSQ9LwMUPdlVJAUxG+ZJwyWSnTQTWNZzCqvpmP88XNQjXSY3J5SuHy5dqmBUQt/PjL1W3OR4hmzyR9KjxbxbsuC/ubw2y3Qokk502FogXQcXpn6V81Bua7HjvxEVdvyNcJ6nrzvosAKb3ldZAuXiDRJ5IetTmCZcrCWcycOju8/iiZCvHZ0GcfkRKwMQLgMmWo1wrUtGmVbtbANGCt3gRVVuZ7etw175nSl0jqkoKsGnBeGw+eBZ2hyto8T1woGcFvsmlvEgESOSJlECLf3PgoDDEbIKzz+Ob4dsdLmw93gPrCLvkoCAOlwcQUih9vKN2cJMqri7lysgH/KsFsYgL/bxpwXif+6vSYFtx182Sbw8Vd92sozXxA4k8QUggHhSm1DUGudn19vO+gBlWuLywAMjal2giHyiSM8bmYa/Nrmpwi6TJQ1hbCbTZB/az0kBfUzoewIANvp/nYeQ4VNx1s297okIiTxAKKGUf1JOdMNEWcaXeVt4/cTFoxi03uEUCweTCCnbT2s81peMTXtQDIe8aglBgyLWgmUCERTvWguyIHLPsvkRC6m2FNTf/yuGKyiAm5I4BwLThJ1o/RwKayROEDA1Ndjj7pNMKCwt8gWYLwH9RLxEzF4ppaLKrdl8Ergur1DFGjoOX53XZ3AXSDMB/lk3yM6dJfR8HJFQ/RwqayROEDJsPnpVMdyBgd7iw12bHwslWyeyE8Za5sKHJjmV7LqoumiGYabQwY2weM/vnYHMaXl08iVln18hx4ABkmqSlyZJuxKopeX79x3pr4JEci9uhQjN5gpBBjdlBXGlKisAFPyGKU8o3PJKullJ29ZX1zXhxfys2zBsn+VtyqQFY+YAOn2n32bWr97X6LVp3dLtRtacFJkOwgcVsMvoNgKz+aGtr8zuOlV2SNZCkGiTyBCGD2vS0am3QLHfLzy5ckfVU0Sr+UgLJEuyObjfTrVPuvORs8sJ3bT54Nsgzyd3PB70d5ZhNqP6B/0Cj1u01UYt5RAsSeYKQQU3UJKB+gY/lbim47QVur97Xil6PV9bPXq1ro9w5iL1ixN+Vk2liRgCzgofEfaF28LMMStP91qI22C1VIZEnCBkCBSQn04SuHo9fII+WWSNL9Fh+5FJpcMX+31pcG1miLBA4GNgdLkmzirjNZpNRdgYdjjehwEEsMNoYSMxiHtGCRJ4gFJCyqdd+eBrtTo/mWaNa0VNCKEQuFUnKknEpURZj5LigfXIFNoTPC4NHYD53IPQ3IalBTBxtTChDIk8QGiktsqIg4yoKA6eTMgizUS0CbzJyyBqUxjSX8NAWSSqI8Jo9zeiV0FytUanC54XBg5UPCND/JiRl3hJHGxPKkMgTRISRSnimBkt6GuZMuEnS/KKEVDKuGWPzrhXdkD5GyZwjh5a6qFq8iPREExP+6BL5np4eVFVV4ZtvvoHFYsFLL72E3Nxcv8888cQT6OjogMlkwqBBg7B9+3ZcuHABa9euBcdxuPXWW7FhwwYYDOSqTyQ3ShWKWDhcbuy12TULvNlkxMLJVhw+085cjJVCyZyjhCC8SiKuxX7OMm9RJKt6dIn8zp07MWbMGDz11FM4cOAAtm3bhnXr1vl95sKFCzhw4AA4UZrOTZs2YeXKlbjrrruwfv16/OEPf8CsWbNCOwOCiHP0zjqlbORyn/XyPHNmPKWuUfG7rCJXS0Ggu0XZN5UYkWOWzcipx7wiZdMfZOTIPVIDukTeZrNh+fLlAIBp06Zh27ZtfvsvX76Mq1ev4vHHH8fVq1fx6KOPYsaMGWhtbcWdd97pO+7YsWMk8kTSo2ex1WTkZCNtA9myaKKsiCoNNGKbeqBpJSi3vpEDeP9FWSGP++pdLZKuoHpt6FLukZXjs8gerwFFkd+9ezd27Njht23YsGHIzs4GAFgsFnR2dvrtd7vdeOSRR7B06VJ8++23qKiowIQJE8DzvG9mL3WcQGBEWyTo6emJyu9ECmp/bNHS/srxWdj8R3mRNXKAoOmDBxnw2J3DsONkBy45pfPmiBk8yICCjKtoa7vK/EyeJY35XcMtaVhWPFTyOwoygBV352LHyQ60Oz3Iu/ZZAH7tE2SdZdP/yuHSfb0LMoDt82/y/Z1K9044UBT5srIylJWV+W1bsWIFnE4nAMDpdGLw4MF++2+44QaUl5cjLS0Nw4YNQ2FhIc6fP+9nf5c6TkCL14Je2traovI7kYLaH1u0tL+wENhu+x9Zs0d6mjEop411hPKCrcnAYWPpBBQWys9sn587WDIqVE0encJC4Mk5wdufnANVxbWBgUye4breqXTvaMFms0lu17XqWVxcjCNHjgAAjh49ismTJ/vtP378OH7yk58AGBDzv/zlLxg1ahRuu+02fPzxx77j7rjjDj0/TxAJx4Z542QLhbvc/Xhxf6vftsDkZkMzTX6Ju3LMJmwuCzbTCLlxxEnIIpUoTe16Q4JX0EtodNnkKyoqsGbNGlRUVMBkMmHLli0AgJdffhkPPPAApk+fjj/96U9YtGgRDAYDnnnmGeTm5mLNmjV44YUX8Morr2DUqFEoKSkJ68kQRLyiplB4R7fbJ8ji48TJyxzdbsmgIwGlhU8hwVe4ZpJq1xvULt5Gk1SpvatL5M1mM7Zu3Rq0/dlnn/X9/9///d+D9t9yyy1477339PwkQSQ8gsjKmTikFii1eKzIlSKMhICpjWjlgKABTIpoCW+4vYDiGXJSJ4goI+f+J2X+UKohq3S83PZQkTIpScEDku0VIwiv3eECj+vCq5TzXg9a+jTRIZEniChTWmRFjkJJQTFahDsW5QZLi6w4tnYmztfNQdP6+5mfUxpo1Aiv1qInWtuSjJG0JPIEEQOqfzAuqHISK4eLFuGWqsgU7dzqrGIdSgONkvAKM/1LTk/IM/1kqb2rBhJ5gogBWrxdtAh3PJQb1DvQKAlvOE0s8TAYRgtKUEYQMUJtDhetRTFinVtdbxEPpQpP4TSxpFKhERJ5gkgAYi3cWtHTXiXhDXeyskTrU72QyBMEETfICS/VctUHiTxBEAmBIP56q3KlKiTyBEEkDHqqcqU65F1DEASRxJDIEwRBJDEk8gRBEEkMiTxBEEQSQyJPEASRxHA8z6jXFSNY1U0IgiAIeQILOAFxKPIEQRBE+CBzDUEQRBJDIk8QBJHEpJzI/+///i9Wr14tuW/Xrl1YsGABFi1ahMOHD0e5ZfL09PTgqaeeQmVlJX784x/jypUrQZ954oknUF5ejiVLlmD58uUxaKU/Xq8X69evx+LFi7FkyRJcuHDBb3889zeg3P6amhosWLAAS5YswZIlS9DZ2RmjlsrT0tKCJUuWBG1vbGzEwoULsXjxYuzatSsGLVMHq/2//vWvMWfOHF//nzt3LgatY+N2u1FVVYXKyko8+OCD+MMf/uC3P2r9z6cQP/vZz/iSkhJ+5cqVQfsuXbrEz507l+/t7eWvXr3q+3+88F//9V/81q1beZ7n+Q8//JD/2c9+FvSZ73//+7zX641205gcPHiQX7NmDc/zPN/U1MQ//vjjvn3x3t88L99+nuf58vJy/ptvvolF01Tz1ltv8XPnzuXLysr8tvf19fH33Xcf73A4+N7eXn7BggV8e3t7jFrJhtV+nuf51atX86dOnYpBq9SxZ88evqamhud5nu/o6OCnT5/u2xfN/k+pmXxxcTGqq6sl933++ecoKipCeno6srOzkZ+fjzNnzkS3gTLYbDZMnToVADBt2jR89NFHfvsvX76Mq1ev4vHHH0dFRUVczIzFbZ40aRJOnz7t2xfv/Q3It9/r9eLChQtYv349ysvLsWfPnlg1U5b8/Hy8/vrrQdu/+OIL5OfnY8iQIUhPT8fkyZPx6aefxqCF8rDaDwCtra146623UFFRgV/+8pdRbpkyDzzwAH7yk58AAHieh9F4vUhJNPs/KROU7d69Gzt27PDbVltbi9mzZ+Pjjz+WPKarqwvZ2dm+vy0WC7q6uiLaThZS7R82bJivfRaLJcg04Ha78cgjj2Dp0qX49ttvUVFRgQkTJmDYsGFRa3cgXV1dyMrK8v1tNBrh8XiQlpYWV/3NQq793d3deOihh/Cv//qv6O/vx9KlS3H77bdj7NixMWxxMCUlJfjb3/4WtD0R+h9gtx8A5syZg8rKSmRlZWHFihU4fPgwZsyYEeUWsrFYLAAG+vrpp5/GypUrffui2f9JKfJlZWUoKyvTdExWVhacTqfvb6fT6XcRoolU+1esWOFrn9PpxODBg/3233DDDSgvL0daWhqGDRuGwsJCnD9/PqYiH9inXq8XaWlpkvti2d8s5NpvNpuxdOlSmM0DBSvuvvtunDlzJu5EnkUi9L8cPM9j2bJlvjZPnz4df/7zn+NK5AHg66+/xpNPPonKykrMmzfPtz2a/Z9S5ho5JkyYAJvNht7eXnR2duKLL77AmDFjYt0sH8XFxThy5AgA4OjRo0FBD8ePH/e9GjqdTvzlL3/BqFGjot5OMcXFxTh69CgAoLm52a8/472/Afn2//Wvf0VFRQX6+/vhdrtx8uRJjBs3LlZN1czo0aNx4cIFOBwO9PX14bPPPkNRUVGsm6Warq4uzJ07F06nEzzP4+OPP8btt98e62b5cfnyZTzyyCOoqqrCgw8+6Lcvmv2flDN5LbzzzjvIz8/HvffeiyVLlqCyshI8z2PVqlUYNGhQrJvno6KiAmvWrEFFRQVMJhO2bNkCAHj55ZfxwAMPYPr06fjTn/6ERYsWwWAw4JlnnkFubm5M2zxr1iwcO3YM5eXl4HketbW1CdPfgHL758+fj0WLFsFkMmH+/Pm49dZbY91kRfbv34/u7m4sXrwYa9euxY9+9CPwPI+FCxfixhtvjHXzFBG3f9WqVVi6dCnS09PxT//0T5g+fXqsm+fHL37xC1y9ehXbtm3Dtm3bAAy8pbtcrqj2P0W8EgRBJDFkriEIgkhiSOQJgiCSGBJ5giCIJIZEniAIIokhkScIgkhiSOQJgiCSGBJ5giCIJIZEniAIIon5/8BaBVNdVDHaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew, ynew = gmm16.sample(400)\n",
    "plt.scatter(Xnew[:, 0], Xnew[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A GMM is convenient as a flexible means of modeling an arbitrary multidimensional distribution of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### How Many Components?\n",
    "\n",
    "The fact that a GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n",
    "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid overfitting.\n",
    "Another means of correcting for overfitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n",
    "Scikit-Learn's `GaussianMixture` estimator actually includes built-in methods that compute both of these, so it is very easy to operate using this approach.\n",
    "\n",
    "Let's look at the AIC and BIC versus the number of GMM components for our moons dataset (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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68g1OXExXL5fU690nr5Cdd/vgvzp2FvjcEeyujtYs3Hyck5fSmdq7Gc/f56O32SclqdkhDuqQyoZJcDEOuP2P8oi/G/M3xLLiwFkJcSGMUL5WYfLKw5hoNLw71B8TEw2WJqY0c7GnmYt9kX0TUzM5cSntdsBfTOeXw0lcz1JPM+lsa0HY2EC9zz4piYS4b3/YOFntjbs8VtDsYGVOv5au/BKVxKyHm2NtYZgvLYQQ5bN0Zzz7Tqfw3lB/Gjjde9aIqYkGz9o2eNa24X7f+gXtiqJwKT2b+EsZNK5nR207S12XXWY1+4tNALt64NmlyFRDUIdU0rLz2BSdbIDChBDl9c+FNN7dfJxezeszuF351y3RaDTUs7ci0Lt2lQxwkBBXNR8Al+KwuB5fqDnQy5lGtW1YIXPGhTAauflaXl4ZhZ2lGW8NalXtJyZIiAP4PQKA/dmthZo1Gg1DAzzYG5/C6csZhqhMCFFGi/46QXTidd4c2Io6VbT3XJkkxAEcXMGjEw7nthbZNLidOyYaZIlaIYzA4bNX+WTrCQa1bUCfli6GLkcvJMRvaT4Aq6v/wpWThZpdHK3o0aweqyPPkZevvcudhRCGlp2nDqPUs7dkzqMtDF2O3kiI33JzSKXYLzgDPLiYls2v0XLWHyGqqm8PpnDyUgb/G9K6ShyEoy8S4rc4eZDp3KLYEH/Qrx4t3Bx4/ZdYrt3QzXnyhBDlt+vkZdbFXWd054Z0a1LX0OXolYT4Ha573A/JUep6KncwMzXhncGtSb2Rw/yNsQapTQhRvLSsXKauOoKbvRnT+/oauhy9kxC/Q5p7T/VG7Poi21o2cGRcd29WR55jxz+X9FyZEOJu5m+IJflaJlOC6mFjUfOOX5QQv0OunRu4til2SAVgwgNN8K5ry4y1R8nIztNvcUKIIv6MvcDKA+d47j4f/OpZGbocg5AQ/6/mA9QTKF8tOqXQytyU/w1uTdK1TN79/bgBihNC3JKSkcP0tUfxdbHnpQebGLocg5EQ/6/mA9TruF+K3RzQyJnRnRry3e7TRCak6LEwIcQtiqLw2rqjXMvM4YPgNgY7IUNVICH+X7V9oH6ruw6pAEzt44ubozXTVh8hK7fsC8sLISpm/eEkfj16nkm9muLn6mDocgyqVCG+ZMkSgoODGTRoEKtWrSIhIYHhw4fz+OOPM2fOHLRa9SCYxYsXM2TIEEJCQjhy5EgJj1qFNX8Uzu6B60nFbrazNOPNQa04eSmDxX+d0HNxQtRs569lMWtdNO08nRjX3cfQ5RhciSG+d+9eDh06xLJlywgLC+P8+fO89dZbTJw4kR9//BFFUdiyZQsxMTHs27ePVatW8f777zNv3jx91K8bBUMqG+66y31N6zK4nTufbz9JTNI1PRUmRM2mKApTVx8mN19h4bA2mFaREzMYUokhvnPnTpo2bcr48eN57rnn6NGjBzExMXTs2BGA7t27s2vXLiIjIwkKCkKj0eDm5kZ+fj4pKUY6Zly3GdT1veeQCsCs/n442Zjzypojcki+EHoQvvcMf/97mZn9fPGqY2vocqqEEkM8NTWV6OhoPvroI+bNm8eUKVNQFKVgeUdbW1vS0tJIT0/Hzs6u4H632o1W8wGQEAHpF++6i5ONBa8PaEl04nW+2hl/1/2EEBV3+nIGb26Mo1uTOozs1NDQ5VQZJc6Md3JywtvbGwsLC7y9vbG0tOT8+dtriGRkZODg4ICdnR0ZGRmF2u3t7Ys8XlxcXCWVXvmysrIK6rO0aoU3Cslbv+Rq40F3vU8jU4Uunja8v/k4PpbpuDsWPcGqLuqriqS+ipH67i5fqzDttyRMUHjG34Zjx44V2aemvn4lhnj79u35/vvveeqpp7h48SKZmZl07tyZvXv3EhgYyI4dO+jUqROenp68++67jB07lvPnz6PVanF2di7yeH5+fpX+S1SWuLi42/UpvnCgMa4pe3H1e/We9/vQ3ZsH39/Ol1E3WP5sa52dQLVQfVWQ1FcxUl/xFEVh8V8niL2UzQfB/nRv617sftX59YuMjLzrthJDvGfPnuzfv58hQ4agKAqzZ8/G3d2dWbNm8f777+Pt7U3v3r0xNTUlICCA4OBgtFots2fPLlexVYZGow6p7PwQMq6Abe277lrPwYrX+jdn2uoj/LDvDKPkv3pCVIq45Ou8sTGOnScu06+VC4+1Kf+p1qqrUi00MG3atCJt4eHhRdpCQ0MJDQ2teFVVRfMB8PdCOL4R2o2+565D27uzPiqJt3+N437feiWemFUIcXcXr2excPM/rIw8i4OVOXMeac6IwIbV/lRr5SEH+9yLS2uo1ajEWSqgnsrtrUGt0Crw6k9HURRF9/UJUc1k5uSzaMu/9HhvG2sPnWNMVy+2T+3BU129sDCTuCpOzVvyqyxuDans/gQyU8G61j1393C2YWrvZry+IZafo5J4rK3810+I0tBqFX4+nMj/fjtO8rUs+rRwYXpfXxrJNMISyZ+2kjQfANo8OL6pVLs/0aUR7TydmPdLDJfTs3VcnBDGb198Co99GsGkFYepY2fJimc78fmo9hLgpSQhXhK3duDoUaohFQBTEw3vDG5NRnY+c9fH6Lg4IYzX6csZPBcWybAlu7mUps48+Xl8VwK97z6JQBQlwykluTWksu8LyLoGVo4l3qVJfXtC72/Mwj/+4VH/8zzUomacdVuI0rh2I5eP//qX73efxtzUhMm9mvJ0N2+sLWruSoQVIT3x0mg+APJz4OjqUt/luR4++LrYM+vnaK5lynk5hcjN1/JNRDz3vbeVpRHxDG7nzrYpPQh9oIkEeAVIiJeGewf1svMDyMsp1V3MTU14d4g/l9KyeXtT1T2KTAhdUxSF36LP0/uDHcz7JZaWbo5sDO3G24NbU8+hZp6NpzJJiJeGRgM9psO1sxD1Q6nv1srdkWe6e7Ns31l2nbiswwKFqHq0WoVNR5Pp9/FOnguPRKOBb57sQNjYjjR3q9lrgFcmCfHS8nlA7Y3/vbDUvXGASQ82pVFtG6avPcqNHDkvp6j+8rUK6w8n0eejHTz/w0GycvNZONSf3yd2p6dvPTlgp5JJiJdWOXvjVuamvD24NWdSbhC2O0GHBQphWHn5Wn46dI5eH2xnwrJDaBX4KKQNf758H4Pbu2NmKnGjCzI7pSzu7I23GQFmpVuxsJN3bTp5O/P97gTGBnnJm1lUK7n5WtYdSuSTrSc4feUGvi72fPJ4O/q2dNHZYnDiNkmTsijUGy+6dsy9PNXVi8SrmfwRe0FHxQmhXzl5WpbtO0PP97YxdfURbC3NWDKqPb9O6MbDrV0lwPVEeuJldas3vmMhtBlZ6t74g3718XC25puI0/Rt5arjIoXQney8fFYeOMdnW0+QdC0Lf3dH5j3agvtlvNsgpCdeVrd649fPlak3bmqi4YnOjdh3OoXoRDknpzA+2Xk353n/bxuz1kXj4mjFd2M6sm58Vx7wqy8BbiAS4uVxZ2+8DDNVhgZ4YGNhyjcRp3VXmxCVLD07jy93nOKpNWeZ90ssnrVt+OHpQNY834X7mtaV8DYwGU4pj1u98fDBam88YEyp7uZobc6Q9u4s33eW6X19qWtvqeNChSi/S2nZfLsrnrDdCVzPysPfxYrPHu1AJ1nbpEqREC+vco6NP9GlEd/vTuDHvWd46cEmOi5SiLI7fTmDL/4+xerIc+Tma+nTwoVx9/lgmZ6MnwR4lSMhXl4aDfSYAeGDytQb96lrR49mdQnfm8DzPXxkoXtRZRw5d5XPt59kU/R5zE1MGNzenWe6eeFd1w6AuLhkA1coiiMhXhE+94N7xzL3xp/q6sUTS/ex8WgSA+9y0lch9EFRFHb8e5nPt51k96kr2FuZ8dx9PjzVtRH17GVdE2MgIV4RBWPjZeuNd29SB5+6tnwTcZrH2jSQL4aE3uXla9l4NJnPt58iLvk69R0smdnPl+EdPbG3Mjd0eaIMJMQrqhy9cY1Gw5NdvZi1LpqDZ1Jp39BZD4UKoZ7DcuWBs3z59ynOpWbiU9eW/w1pzYA2bliayXKwxkgGZCuqnPPGB7drgIOVGUtluqHQg9SMHD788x+6vL2FOetjqO9gxZejA/hj0n0MC/CQADdi0hOvDOXojdtYmBHS0ZOvd8aTdDUTNydrPRQqapq45Ot8t+s066ISycrV8qBfPcbd50OHRvK/v+pCeuKVoZy98dGdG6IoCmF7ZHVDUXny8rX8Fp1M8JLd9P3ob9ZFJTKwbQM2T+rOV090kACvZqQnXlkK9cZHgFnJB/K417LhoeYuLNt3hgn3yymqRMWkZuSwfP9ZwvckkHg1kwZO1szo60twBw+cbEo3c0oYHwnxynLnTJVD4dBhbKnu9lTXRvwWc551UYkM7+ip4yJFdRSbdHvIJDtPS2fv2sx+pDkP+tXHVFYSrPYkxCvTrd743+9D25Gl6o139HKmuasD30TEE9LBQ6YbilLJy9fyR+wFvtl1mn3xKViZmzConTtPdmlEMxd7Q5cn9EhCvDKVozeu0Wh4qmsjpq4+wq6TV+jauI4eChXGKiUjh+X7zxC+O4Gka1m417JmZj9fhgXIkElNJSFe2XzuB4/AMvXGH/F34+1Nx/gmIl5CXBTr2PnrLN0Zz89RSWTnaenauDZzH23BAzJkUuOVKsQHDhyInZ26foK7uzvBwcG88cYbmJqaEhQUxIsvvohWq2Xu3LkcP34cCwsLFixYQMOGDXVafJV0qzceNrDUvXErc1NGBHqyaOsJEq5k0LC2rR4KFcYgMyef9/84ztc747E0M2VIe3ee6NKIpvVlyESoSgzx7OxsdRpcWFhB24ABA1i0aBEeHh48++yzxMbGcu7cOXJyclixYgVRUVG8/fbbfPbZZzotvsry7lnm3vjITg35bPtJvt11mjmPtNBDkaKq23vqCq+sOcLpKzcYEejJtN6+ONrIIfGisBLniR87dozMzEzGjBnD6NGj2b9/Pzk5OXh6eqLRaAgKCmLXrl1ERkbSrVs3ANq0aUN0dLTOi6+y7pw3fqh088brOVjxcCtXVh04R1pWro4LFFVZenYes3+OJviLPWgV+PGZQN4Y2EoCXBSrxJ64lZUVY8eOZejQoZw+fZpnnnkGBweHgu22tracPXuW9PT0giEXAFNTU/Ly8jAzq6HD7uXojT/V1Yt1UUmsjjzHU1299FCkqGr+/vcS09ccJelaJmO6ejGld1NsLGroZ0iUSonvDi8vLxo2bIhGo8HLywt7e3uuXr1asD0jIwMHBweysrLIyMgoaNdqtcUGeFxcXOVUrgNZWVmVWp+t9+N4bn+J5E3vcbXxoBL3twD86lry5bZ/6FgrE5P/TDes7Poqm9RXfhk5Wj7fe5E/T53C3cGc9/q40byehoST/xq6tAJV+fWDmltfiSG+evVq/vnnH+bOncuFCxfIzMzExsaGM2fO4OHhwc6dO3nxxRc5f/48W7dupV+/fkRFRdG0adNiH8/Pz6/Sf4nKEhcXV7n1+frCqR9x/fdHXPtOKVVv/IUcR0KXHeK8pjYP+NXXbX2VTOorny1xF3h1YzQX07J4vocPLz3QBCvzqnf0blV9/W6pzvVFRkbedVuJIT5kyBBmzJjB8OHD0Wg0vPnmm5iYmDBlyhTy8/MJCgrC39+fVq1aERERQUhICIqi8Oabb5ar2GqlHDNV+rR0wcXBim8iThcJcVG9pGbk8PqGWH46lEiz+vbM6FabAd18DV2WMDIlhriFhQULFy4s0r5y5cpCP5uYmPD6669XXmXVRRnHxs1NTRjVuSHv/n6cfy6kyVSyamrT0WRm/RzN1Ru5vPRAE8b3bMzJf48buixhhGQVQ127c6ZK9JpS3eXxjp5Ympnwjaw1Xu1cSsvmhR8ief6Hg7g4WrH+xSAm9Woq51oV5SbvHH3w7gnO3nB4Wal2r2VrwcC2Dfjp0Dmu3sjRcXFCHxRF4eeoRB76YDt/xl5kWp9mrHuhK83dHEq+sxD3ICGuDxoNtA6G+L/hWmKp7vJk10Zk5WpZtu+sjosTuhadeI0x3+7npeVRNKpjy68vBfFCj8aYmcrHT1ScvIv0pdVQQIGjq0q1u6+LA118ahO2+zR5+Vrd1iZ0IursVcZ+u5/+i3ZyICGV1x72Y/VzXWhcT77nEJVHQlxfavuoy9QeWQGKUqq7PNXVi6RrWfwec0HHxYnKdOB0CqOX7uOxTyKIPJPK5F5NiZh+P09385bFqkSlk0PB9Mk/GDZOhgvR4NKqxN3v962Hp7MN30TE83BrVz0UKMpLURT2nErh4y3/svvUFWrbWjC9ry8jOzXEzlI+ZkJ35N2lTy0GwabpcHh5qULc1ETDE10aMX9DLEfPXZN/rCpIURT+/vcyi/76l/2nU6lrb8lrD/vxeKCnHC4v9EKGU/TJxhmaPARHV4M2v1R3GRrgjq2FKd9ExOu4OFEWiqLw17ELDPx0F6OX7uNcaibzHm3B39N68nQ3bwlwoTfyTtM3/2A4vhHit6snkCiBg5U5QwM8+GFvAoObeOihQHEvWq3C5tgLLN76L9GJ13GvZc2bA1sxuH0DLM2q3qHyovqTENe3Jr3B0hEOryhViAM82aUR4XsS+HTPZbq0VeQ8nAaQr1XYFJ3M4r9OcOx8Go1q2/C/Ia0Z2LYB5jJVUBiQhLi+mVtBi8fUIZWc98Gi5LP4NKpjy/S+vizYGMfXO+N5upu37usUKIrC8Qtp/HokmV+OJBN/OQOfurZ8GNyG/q1dZZ63qBIkxA2hdTAc/A6ObYTWw0p1l7FBXvx1NIG3Nx2jjYcTAY2cdVxkzaQoCjFJ19kUncymo+c5dTkDEw109HJm8kNN6dvSVaYJiipFQtwQPDuDo6c6S6WUIa7RaHi5az2mbL7I+B8PsnFCN+rYlby0rSiZoigcTbzGr0fPsyk6mYQrNzA10dDZuzZju3nRu4WLvNaiypIQNwQTEzW8d74PaRfAvnRLztpamPDpiPYM/DSCl5Yf4vsxgdIrLCdFUYg6e5VN0ef59Wgy51IzMTPR0KVxHZ6/z4eHWrjgbGth6DKFKJGEuKG0Doa/34Po1dB5fKnv1tzNgfmPtWTa6iN89Oc/vPxQMx0WWb1oFYXIhBQ2HjnPb9HJJF3LwtxUQ1DjOrz0QBN6Na+Pk40EtzAuEuKGUrcpuLVVh1TKEOIAwwI8OHA6hY//OkHbhrXo2ayejoo0flqtwqGzqfxyOJlfDp3lSmY8FqYmdG9ahym9m/GAX30creUExMJ4SYgbUutg+G06XIyDemU7bdPrA1pyNPE6k1ZEsSE0CPdaNjoq0vjc+nLyl8NJbDiSTOLVTCzMTGjvakVI16bc71sPeysJblE9yBwpQ2o5BDSm6qJYZWRlbspnI9qRn68w/sdDZOeV7gjQ6uzfC2m8v/k49y/cTv9FO/l6ZzzNXOz5INifyNceZPb9Lgxo00ACXFQr0hM3JLu60PgBOLIK7p+tfuFZBo3q2PLuUH+eC4/kjY1xvD6gpY4KrboSrmSw4UgyvxxO4tj5NEw00NmnNuO6e9OnpYuMcYtqT0Lc0FoHw5qxkBABXt3KfPc+LV14ppsXX/4dT/uGtRjQpoEOiqxakq5msvFIMr8cSeLIuWsABDSsxbxHW9C3lQv17K0MXKEQ+iMhbmjN+oGFHRxZXq4QB5jWx5eos1eZsfYoLdwcquVJBy6nZ/PrUbXHvf90KgCtGjgys58vD7d2o4GTtYErFMIwJMQNzcIG/B6F2PXQ7z0wL3sYmZuasPjxdjz88d88F36Qn8d3xbaarGGdeDWTT7eeYOWBs+TmKzStb8fkXk3p7++GV52SlywQorqrHp90Y+cfDId/hOOboOWgcj1EfQcrPgppy6iv9zJj7VE+Cmlj1AtlnUu9wafbTrLqgHqO0WEBHozu3IhmLtXvfxlCVISEeFXQqBvYu6mzVMoZ4gBdG9fh5V5NeW/zP3TwcmZUp4aVWKR+nEu9wSdbT7I68iwaNAR38OD5Ho1luESIu5AQrwpMTKHVENjzKWRcBts65X6oF3o0JjIhlfm/xNK6gSP+Hk6VV6cOnU25wafbTrDqwDlMNBpCOnjyfA8f3CS8hbgnmSdeVfiHgDYPotdW6GFMTDR8ENyGuvaWvPDDQVIzciqpQN04m3KD6WuO0PO9bayJTOTxQE+2T+vB/MdaSoALUQoS4lVF/RZQv5U6S6WCnGws+HREOy6mZfHyyii0WqUSCqxcZ67c4JXVanivPZTIiJvh/fqAlrg6SngLUVoynFKVtB4Gf8yCyyegTuMKPZS/hxOz+zdn1s8xfLb9JON7VuzxKsuZKzdYvPVf1hxMxNREw8hODXnuPh9cHGVutxDlISFelbQaCn/MVr/gvP/VCj/cyE4NOZCQysLNx2nj4UTXxvcea8/L15KenUda1q1LLmlZeaRnqxcAc1MNZiYmmN1xfastKTmTNKsUta1gHw1mpibcyMnj24jTrD2khveoTg15vocP9R0kvIWoCAnxqsTBFbzvU0O850yo4BRBjUbDmwNbEZN0nQnLDjGgTQPSsnJvB3X2HUGdlUdmbmWsv5J81y2WZiaM7qz2vCW8hagcpQrxK1euMGjQIJYuXYqZmRnTp09Ho9HQpEkT5syZg4mJCYsXL2bbtm2YmZkxc+ZMWrdurevaq6fWIbDuOTi7Fzw7VfjhbC3N+HxkO0Z/vY+VB85ib2WGnaUZ9lZmOFqb417LGvubP9tZmqvXVmY4/Odnu5sHD+Xma8nXKuTmK+RpteTlK+RpFfLytZyMP42bu8fNn9W2XK1CvlaLVgvdmtShnoS3EJWqxBDPzc1l9uzZWFmpH7633nqLiRMnEhgYyOzZs9myZQtubm7s27ePVatWkZycTGhoKGvWrNF58dWS3yOw8WV1nfFKCHGAxvXs2TXjgUp5rHuxzbyAX5O6On8eIcRtJc5OeeeddwgJCaFePfXEAzExMXTs2BGA7t27s2vXLiIjIwkKCkKj0eDm5kZ+fj4pKSm6rby6srQD34ch5ifIyzZ0NUKIKu6ePfG1a9fi7OxMt27d+OKLLwB1wf1bh3Pb2tqSlpZGeno6Tk5OBfe71e7sXPSM7HFxcZVYfuXKysqqEvXZ1uqCZ9Yqzm1dSpp7j4L2qlLf3Uh9FSP1VUxNre+eIb5mzRo0Gg27d+8mLi6OV155pVAPOyMjAwcHB+zs7MjIyCjUbm9f/BoXfn5lO4ONPsXFxVWN+po2gci3cL+yE3o9X9BcZeq7C6mvYqS+iqnO9UVGRt512z2HU3744QfCw8MJCwvDz8+Pd955h+7du7N3714AduzYQUBAAO3atWPnzp1otVqSkpLQarXF9sJFKZmaqYfh/7sZbsiwlBDi7sp8xOYrr7zCokWLCA4OJjc3l969e9OyZUsCAgIIDg4mNDSU2bNn66LWmqV1MOTnQOw6Q1cihKjCSj1PPCwsrOB2eHh4ke2hoaGEhoZWTlUCXP2hTjM4vAICxhi6GiFEFSVrp1RVGo26zvjZPZASb+hqhBBVlIR4VdZqmHp9dJVh6xBCVFkS4lWZkwc0DFIPw1eq3kqEQgjDkxCv6vyD4coJSDxo6EqEEFWQhHhV5/comFpWyjrjQojqR0K8qrN2gmZ9IXqNeuYfIYS4g4S4MfAPgRtXsE/629CVCCGqGAlxY9D4QajdmLpHPof8XENXI4SoQiTEjYGpOTy0AMu0BDiw1NDVCCGqEAlxY9G0Dxn1A2Drm7KeihCigIS4sdBouNDmJci+Dtv/Z+hqhBBVhIS4Ecl2agLtRsP+L+Hyv4YuRwhRBUiIG5uer4KZNWyeZehKhBBVgIS4sbGrB90nwz+b4ORWQ1cjhDAwCXFjFPg8OHnC76+CNt/Q1QghDEhC3BiZW0Gv+XAxBg5+b+hqhBAGJCFurJoPAM8usPUNyLpu6GqEEAYiIW6sNBro/QZkXIK/Fxq6GiGEgUiIG7MG7cB/OOz5VM7+I0QNJSFu7B6YDSZm8OccQ1cihDAACXFj5+AGXSdC7M+QsMvQ1Qgh9ExCvDroEgoODeC3GaDVGroaIYQeSYhXBxY28MAcSI5Sz8cphKgxJMSri1ZDoUF72DIPcjIMXY0QQk8kxKsLExPo/RakJUPER4auRgihJxLi1YlnILQYBBEfw7VEQ1cjhNADCfHqptc8ULTqsIoQotqTEK9unDyhy4vqF5znIg1djRBCxyTEq6OgSWBXH36fAYpi6GqEEDpkVtIO+fn5vPbaa8THx6PRaJg3bx6WlpZMnz4djUZDkyZNmDNnDiYmJixevJht27ZhZmbGzJkzad26tT5+B/FflvZw/2uwPhRi1kLLwYauSAihIyWG+Nat6okHli9fzt69e/nggw9QFIWJEycSGBjI7Nmz2bJlC25ubuzbt49Vq1aRnJxMaGgoa9as0fkvIO6izQjY9wX8MReaPawuXytETZRzA36ZALb1oMd0sHIwdEWVqsThlAcffJD58+cDkJSUhIODAzExMXTs2BGA7t27s2vXLiIjIwkKCkKj0eDm5kZ+fj4pKXJWdoMxMYXeb8K1M7DnE0NXI4Rh5NyAZcFwdLW6UNziDhDzU7UaZiyxJw5gZmbGK6+8wh9//MHHH39MREQEGo0GAFtbW9LS0khPT8fJyangPrfanZ2dCz1WXFxc5VVfybKysqpZfXVxb3AfNtvf46RtIPnWtXVWG1TH10+/pL6K+W99mrwsPP6egs3FSJICZ5Pj0AiXA29jvepJ0l07c77dFHLtGhisvspSqhAHeOedd5gyZQrDhg0jOzu7oD0jIwMHBwfs7OzIyMgo1G5vb1/kcfz8/CpYsu7ExcVVv/rqfQCfBNL07HIYsFg3hd1ULV8/PZL6KqZQfTk3YFkIXIyEgZ/TwD9Ebe88APZ9id1fC2j8+wjoPhW6TAAzC/3WV0aRkXefaVbicMq6detYsmQJANbW1mg0Glq2bMnevXsB2LFjBwEBAbRr146dO3ei1WpJSkpCq9UW6YULA6jtA4Hj4FA47P8KstMNXZEQunUrwON3wMDP4VaAgzrM2Ok5eHEfNO0Nf82Hz4PgdIRua9Lh8E2JPfGHHnqIGTNmMGLECPLy8pg5cyY+Pj7MmjWL999/H29vb3r37o2pqSkBAQEEBwej1WqZPXu2zooWZdR9KiREwMbJ6hedrYdC+6fAVWYPiWom5wYsH64G+GOfFQ7wOzm4wbDv4Z/N8Otk+LafOhmg13ywraRhx5wbcPIviPsF/v2d2o1DwO/tynnsO5QY4jY2Nnz0UdG1OMLDw4u0hYaGEhoaWjmVicpj7QTPbIVz++HANxD1IxxYqi6Y1f5JdQqiha2hqxSiQjR5WWqAn9quBnib4SXfqelD0Ggv7HgXdn0Mx39Vg7zNCHU9orLKuqb+YYhbDyf+hNwbYOUEzfpxvUFP6pX9EUtU6jFxYeQ0GvDoqF76vAmHV0DkN+pc8t9fhdbD1EB3aWXoSoUou9xM3HdOhQsHSh/gt1jYwINz1M/Ahpdh/YsQ9QP0/wDqlWIMO/0SHN+o9rhPbQdtLti5QJvHwe8RaNgVTM3J1dGXwhLiNZF1LXVcMHAcnNkDkd/CwTB1zLxBAAQ8pS6kZWFj6EqFKFluJiwLwfbCAXjs07IF+J3q+cGTG+Hwj7B5ljpW3iUUuk8r+lm4ehaObVCD+8xudb2iWo3Uz5Xfo+rnqDw9+XKQEK/JNBpo2Fm99HkLDi9Xe+c/j4ffZoJ/sNo7r9/C0JUKUbybAc6p7SR3fA23No9X7PFMTKDtSGjaF/6YDTs/gOg10O89qOUFx35RgzvpkLp/vRbqd05+j0D9lupnSs8kxIXKxhk6vwCdnlfP1Rn5jdpD3/cFuHe83TuXIz9FVZGbCctujoEP+IRrVu1wq6zHtq0Nj32iDolsmAQ/Dru9rUEAPDhPDe7aPpX1jOUmIS4K02igUVf10ucdOLxMDfR1z8Of89QVEts/BZZ2hq5U1GQFAb4NBnwCbUeALsacG3WF53bCoe/V89f6PgyO+jtAqDQkxMXd2dZWQ7vzePXDsvMD2Pwa7HhP7bF3fFbtwQuhT7mZsPzxwgGuS2YW0OFp3T5HBchStKJkGg349IQn1sPTW9Rv27e9BR+2UkM97byhKxQ1xa0AP7lVPQJZ1wFuBCTERdm4B8DwH+H5XdCsL+z+BD5sDRsmYZ6eZOjqRHWWmwXLR9wR4CMNXVGVICEuyqd+Cxj8FYRGqlO6DoXj8+tQWPssXKy6iyQJI5WbdbMH/hc8ukgC/A4yJi4qxtkbHvkI7nuFlA2vUzvuZ/XUcL79odvL6lGhQpRGbiakJavDc9eT1Ou0ZPVyPhou/6MGeLtRhq60SpEQF5XDwY2LbV+i9oA3YN8S2Pu5ejCEd0/oNhkaBZVuDq1WC3lZ6gc698btS142WDurMwNq4hIBtxZQMsA85HJRFMjPhbxM9d8uNxNuXC4+oG+1ZV0t+jhm1uDgCvaucN80aDVE779KVSchLiqXbW3oORM6v6hOTdy1GL7rr86tdfa+I5gz77jOhJwM9Tovs+TnsK4Fju7g4K6G+n9v27uCqbnuf1ddyc+FS8chOQqSotTr89GQnw1mVmBqoV6bWd68vvXzzTZTyzu2Wd6+oAEUNWAVrfpcBbeVe99GwfXKJThqqYbyneGcl63+4S243GznHiv3aUzV88A6uKrvi4Zdwd5F/be7Fdr2rmDlaDx/uAxEQlzohpUDdH1JnYYY9QPs/xrO7QNzWzC3Vi92Ljdv26iHNd+6XeTaRg2qGylw7SxcS4TriertM7uL9uA0JupjOzYAh5vB7uiOXboJ1MqHWg3V85BWBXk5cCkOkg/jErMVdibAhRg1DAEs7MCltXrkrKXdzZDMuR2WeVmQf8fPmak327PvCNeb1yiARn19NJpibmv+c9vk9m002CgayLC//QfD3Ep9Hc0s1R6zmaX6b1bwB+SO/cyswKb27aC2rasuCysqTEJc6Ja5tTrHVpfzbLPTb4b6OfVy5+0L0fDPb5CXhQfAzpv3sXZWw9yp4X+uG4GTx82eayXLy4aLsTd714fVHvaFGDWEAQdzW2jQTn2tXNuAWxtw9tHbGhwlOVnFTwpRU0mIC+NnaQd1m6mX4igK3LhC/KHteDlp4GoCpCao1+ePqsuP3gxSlUbtLRYKd08wMS/csy00jPDftv9c596AlHh1hTtQhwlc/SHwOfXarS3/XMjCr7msUyPKRkJcVH8aDdjWIat2cyiuJ6nVql+w3Rnut65P71Rn29xtfFdjcnsoodA49R1j0VYO6nWzfjcDu426mNJ/x3plaqYoBwlxIUxMbn4p2gAadim6PS8Hrp9Te/R3foFoZgWm8hEShiXvQCFKYmahzqAQogqqGt+YCCGEKBcJcSGEMGIS4kIIYcQkxIUQwohJiAshhBGTEBdCCCMmIS6EEEZMoyjKPZYaq1yRkZH6eiohhKhW2rcvfm1+vYa4EEKIyiXDKUIIYcQkxIUQwojVuLVTcnNzmTlzJomJieTk5PD888/zwAMPFGz/9ttvWbVqFc7OzgDMmzcPb2/9rpsxcOBA7OzsAHB3d+ett94q2LZy5UqWL1+OmZkZzz//PD179tRrbWvXruWnn34CIDs7m7i4OCIiInBwcABgwYIFHDx4EFtb9RRqn376Kfb2+jkBw+HDh3nvvfcICwsjISGB6dOno9FoaNKkCXPmzMHkjnW5s7KymDp1KleuXMHW1pZ33nmn4N9cH/XFxcUxf/58TE1NsbCw4J133qFOnTqF9r/X+0DX9cXGxjJu3DgaNWoEwPDhw+nXr1/BvoZ+/SZNmsTly5cBSExMxN/fnw8++KBgX0VR6N69e0H9bdq0YfLkyTqrrbhcady4sX7eg0oNs3r1amXBggWKoihKamqqct999xXaPnnyZOXo0aMGqEyVlZWlDBgwoNhtFy9eVPr3769kZ2cr169fL7htKHPnzlWWL19eqC0kJES5cuWK3mv54osvlP79+ytDhw5VFEVRxo0bp+zZs0dRFEWZNWuWsnnz5kL7L126VPn4448VRVGUDRs2KPPnz9drfSNGjFBiY2MVRVGUZcuWKW+++Wah/e/1PtBHfStXrlS+/vrru+5v6NfvlqtXryqPPvqocuHChULtp0+fVsaNG6fTmu5UXK7o6z1Y44ZT+vTpw0svvQSof61NTQufIiomJoYvvviC4cOHs2TJEr3Xd+zYMTIzMxkzZgyjR48mKiqqYNuRI0do27YtFhYW2Nvb4+npybFjx/ReI8DRo0c5ceIEwcHBBW1arZaEhARmz55NSEgIq1ev1ls9np6eLFq0qODnmJgYOnbsCED37t3ZtWtXof0jIyPp1q1bwfbdu3frtb7333+/4Cw5+fn5WFoWPpPQvd4H+qgvOjqabdu2MWLECGbOnEl6enqh/Q39+t2yaNEiRo4cSb169Qq1x8TEcOHCBUaNGsUzzzzDqVOndFpfcbmir/dgjQtxW1tb7OzsSE9PZ8KECUycOLHQ9ocffpi5c+fy3XffERkZydatW/Van5WVFWPHjuXrr79m3rx5TJkyhby8PADS09MLDU3Y2toW+XDpy5IlSxg/fnyhths3bjBy5EjeffddvvrqK3788Ue9/ZHp3bs3Zma3RwcVRUFz86QLtra2pKWlFdr/zteyuO26ru9W6Bw8eJDw8HCefPLJQvvf632gj/pat27NtGnT+OGHH/Dw8OCTTz4ptL+hXz+AK1eusHv3bgYNGlRk/7p16/Lss88SFhbGuHHjmDp1qk7rKy5X9PUerHEhDpCcnMzo0aMZMGAAjzzySEG7oig88cQTODs7Y2FhwX333UdsbKxea/Py8uLRRx9Fo9Hg5eWFk5MTly5dAsDOzo6MjIyCfTMyMvQ23nyn69evEx8fT6dOnQq1W1tbM3r0aKytrbGzs6NTp04G+5/CnWOPGRkZBWP2t9z5Wha3XR9+/fVX5syZwxdffFFkLPRe7wN96NWrFy1btiy4/d/PQVV4/X777Tf69+9f5H/TAC1btiz4risgIICLFy+i6Hg29X9zRV/vwRoX4pcvX2bMmDFMnTqVIUOGFNqWnp5O//79ycjIQFEU9u7dW/BG1pfVq1fz9ttvA3DhwgXS09OpW7cuoPaOIiMjyc7OJi0tjZMnT9K0aVO91gewf/9+OnfuXKT99OnTDB8+nPz8fHJzczl48CAtWhjmnJHNmzdn7969AOzYsYOAgIBC29u1a8f27dsLtt/tQApd+fnnnwkPDycsLAwPD48i2+/1PtCHsWPHcuTIEQB2795d5N/R0K/frbq6d+9e7LbFixfz3XffAerQlKura0GvWBeKyxV9vQdr3ME+CxYsYNOmTYVmnAwdOpTMzEyCg4NZt24dYWFhWFhY0LlzZyZMmKDX+nJycpgxYwZJSUloNBqmTJnC4cOH8fT05IEHHmDlypWsWLECRVEYN24cvXv31mt9AF999RVmZmYFQwDffPNNQX1fffUVmzZtwtzcnAEDBjB8+HC91XXu3DlefvllVq5cSXx8PLNmzSI3Nxdvb28WLFiAqakpY8aM4fPPPyc/P59XXnmFS5cuYW5uzsKFC3UekrfqW7ZsGZ07d8bV1bWg99WhQwcmTJjAtGnTmDhxInXq1CnyPmjXrp1e6lu5ciUxMTHMnz8fc3Nz6tSpw/z587Gzs6sSr9/KlSsBdehz2bJlhXqwt+rLzMxk6tSp3LhxA1NTU2bPno2Pj4/OaisuV1599VUWLFig8/dgjQtxIYSoTmrccIoQQlQnEuJCCGHEJMSFEMKISYgLIYQRkxAXQggjJiEuhB6Fh4cbugRRzUiIC6FHn332maFLENVMjVuKVlRNa9euZfv27WRlZXHmzBmeeeaZYtfEAHV52z///JP8/HyGDx9OSEgIS5cuZePGjZiZmREQEMDUqVNZtGgRCQkJpKamcvXqVUaMGMHmzZuJj48vWPr1pZdeom7duly4cIHu3bszadIkzp07x8yZM8nPz0ej0fDaa6/h6+vLQw89RLt27YiPj6d27dosWrQIrVbLnDlzSEhIQKvVMnHiRAIDA3nkkUfo2LEjx48fR6PR8OmnnxIeHs61a9eYO3cuTzzxBDNmzMDMzAytVsvChQtxdXXV86suqoVyrX0oRCVbs2aNMmbMGEVRFCU+Pl7p3bt3sfvFxMQowcHBSl5enpKdna289dZbyrFjx5QhQ4YoOTk5ilarVcaPH6/89ddfyscff6y8+uqriqIoypIlS5QJEyYoinJ72dCzZ88qgYGBSmpqqpKXl6cMGzZMiY6OVkJDQ5U//vhDURRFiY2NVQYOHKgoiqL4+voqSUlJiqIoSnBwsHLo0CHlhx9+UP73v/8piqIoKSkpSr9+/RRFUZSePXsqkZGRiqIoyssvv6xs2LBBURRF6dKli6IoihIeHq688cYbSk5OjrJr1y7l+PHjlfuCihpDeuKiyvD19QXA1dWVnJycYveJj4+ndevWmJqaYmpqyvTp09m0aRP+/v6Ym5sD6oJH//77L6CuXwFgb29P48aNAXB0dCQ7O7vgOZ2cnAB1bZr4+HhOnjxJhw4dAPDz8+P8+fMA1KpVq6C37OrqSnZ2Nv/88w+RkZEF64zk5eWRkpJS6Llv7XunIUOG8OWXX/L0009jb2/PpEmTKvLSiRpMxsRFlVGaBYq8vb2JjY1Fq9WSm5vLU089hZeXF0eOHCEvLw9FUdi/fz9eXl6lesyTJ0+SmZlJfn4+R44coXHjxvj4+HDgwAEA4uLiCs64U9xjeXt78/DDDxMWFsaXX35Jnz59Cv4oFLe/cnOViy1bttC+fXu+++47+vTpw1dffVXi7y5EcaQnLoyKn58f3bp1Y/jw4Wi1WoYPH46vry99+/YtaGvfvj0PPvhgqZbBNTc356WXXuLy5cv06dMHX19fpk2bxqxZs1i6dCl5eXm88cYbd71/SEgIr732GiNHjiQ9PZ3HH3+80BKk/+Xj48OUKVOYMGECr7zyCp999hlarZYZM2aU6/UQQhbAEjXWf1fFE8IYSU9cVEkrVqxgw4YNRdpffvll2rZta4CKhKiapCcuhBBGTL7YFEIIIyYhLoQQRkxCXAghjJiEuBBCGDEJcSGEMGIS4kIIYcT+D4E/bUuAZQe7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(1, 21)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n",
    "          for n in n_components]\n",
    "\n",
    "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n",
    "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('n_components');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components earlier was probably too many: around 8–12 components would have been a better choice.\n",
    "As is typical with this sort of problem, the BIC recommends a simpler model.\n",
    "\n",
    "Notice the important point: this choice of number of components measures how well a GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n",
    "I'd encourage you to think of the GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Example: GMMs for Generating New Data\n",
    "\n",
    "We just saw a simple example of using a GMM as a generative model in order to create new samples from the distribution defined by the input data.\n",
    "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n",
    "\n",
    "To start with, let's load the digits data using Scikit-Learn's data tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Next, let's plot the first 50 of these to recall exactly what we're looking at (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x288 with 50 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, ax = plt.subplots(5, 10, figsize=(8, 4),\n",
    "                           subplot_kw=dict(xticks=[], yticks=[]))\n",
    "    fig.subplots_adjust(hspace=0.05, wspace=0.05)\n",
    "    for i, axi in enumerate(ax.flat):\n",
    "        im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n",
    "        im.set_clim(0, 16)\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n",
    "GMMs can have difficulty converging in such a high-dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n",
    "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 41)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(0.99, whiten=True)\n",
    "data = pca.fit_transform(digits.data)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n",
    "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(50, 210, 10)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0)\n",
    "          for n in n_components]\n",
    "aics = [model.fit(data).aic(data) for model in models]\n",
    "plt.plot(n_components, aics);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "It appears that around 140 components minimizes the AIC; we will use this model.\n",
    "Let's quickly fit this to the data and confirm that it has converged:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "gmm = GaussianMixture(140, covariance_type='full', random_state=0)\n",
    "gmm.fit(data)\n",
    "print(gmm.converged_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 41)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new, label_new = gmm.sample(100)\n",
    "data_new.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Finally, we can use the inverse transform of the PCA object to construct the new digits (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x288 with 50 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits_new = pca.inverse_transform(data_new)\n",
    "plot_digits(digits_new)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The results for the most part look like plausible digits from the dataset!\n",
    "\n",
    "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits,\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n",
    "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next chapter."
   ]
  }
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